The calculation system

One tool-specific method, selected for each problem — and the same five stages between the number you type and the answer you read.

A clear path from inputs to insight.

One method at a time.
Every assumption in view.

Pipeline · 372 calculatorsEvery stage runs in the tab — there is no calculation serverLast reviewed 2026-10-23

Stage by stage

What actually happens between the control and the result.

Each stage below names the code that implements it. Nothing here is aspirational: if a stage is described, the file that performs it is listed beside it.

Input

the question, captured once

A spec page is an object, not a form. inputs: InputSpec[] declares each control once — key, kind, range, step and default — and initialValues() folds those defaults into a single flat Values record. Every control writes exactly one key back into that record. There is no form library, no per-field state and no second copy of the model.

A slider writes a number. The number input beside it parses the string, ignores an empty field and clamps to the declared range before writing, so a half-typed value never enters the record. A select writes its string value, which compute narrows to a union. The same object then drives the controls, the arithmetic and the charts — one source of truth for all three.

Where it lives

components/engine-shell/EngineShell.tsx — initialValues(), setValue()
components/engine-shell/primitives.tsx — SliderRow, SelectRow, ControlList
components/engine-shell/types.ts — InputSpec, Values

Prepare

check, clamp, normalise

No formula is allowed to see a value outside its domain. Each compute opens with a local num() reader and explicit floors: a vehicle price of at least 500, a term of at least 12 months, a bore of at least 1 mm, a roughness of at least zero. The control already clamped the slider, but the model does not trust the view — a value can also arrive from a deep link, a saved scenario or the terminal.

Units are normalised inside the compute step, on the line that needs them: mm becomes m, m³/h becomes m³/s, mPa·s becomes Pa·s, a percent becomes a fraction. Cross-field constraints are applied last, because those are the cases where two individually valid inputs are jointly impossible — a rod diameter clamped below the bore, a mean coil diameter held above the wire diameter, a target cover above one month.

Three guards sit underneath every page: clamp() maps a non-finite value to the lower bound, div() returns 0 rather than Infinity when the denominator is below EPS = 1e-12, and the formatters print an em dash instead of NaN.

Where it lives

components/engine-shell/core.ts — clamp(), div(), round(), EPS, fmt*
pages/calculators/*.tsx — the first lines of compute(values)
logic/*Worker.ts — the same checks repeated inside the worker

Method

one model, chosen per tool

This is where the calculators stop being interchangeable. Each page declares one primary computational shape and implements that shape first: 251 evaluate a relationship directly, 57 roll a schedule forward period by period, 18 assemble and solve a matrix, 21 iterate to a tolerance, 10 simulate seeded paths, 12 march a field in time, and 3 convert through a factor table.

10 of them run a second shape beside the first — implied volatility beside a closed-form price, a matrix eigen-solve beside a flutter sweep — and the registry records both, because a page that iterates for one output and evaluates in closed form for another is not fully described by either label alone.

The two families diverge inside that choice. Finance models work in money and time — discounting, annuity factors, bond cash flows, option pricing, portfolio moments. Engineering models work in physical units — section properties, Reynolds and Darcy–Weisbach, LMTD, eigenvalue buckling, finite-element assembly, spectral transforms.

Precision is chosen per page, not per family. 10 implementations import Decimal.js and 2 route currency arithmetic through Big.js inside a worker; the remaining 360 work in IEEE-754 doubles, where measurement error dominates rounding error anyway.

Where it lives

pages/calculators/*.tsx — compute(values): EngineResult
engines/<family>/*.engine.tsx — bridge wrappers around a model page
logic/*Worker.ts — the models that run off the main thread
lib/finance/rng.ts, lib/finance/annuity.ts — shared numerical helpers

Compute

on the device, in the tab

The calculation runs in the browser. There is no calculation endpoint: every model is a function in the bundle, so there is no request to intercept, no queue to wait in and no per-calculation cost. A model that would block painting for more than a frame moves into a Web Worker — 6 pages spawn one — so the interface keeps rendering while the arithmetic runs.

Two message protocols exist. The page-local workers take one input object and reply with one result object, and they re-validate that input because a message boundary is a trust boundary: an invalid payload returns { error } instead of throwing across it. The CFD engine worker uses a framed contract — { id, type, payload } — and transfers its velocity profile back as a Float32Array buffer rather than copying it.

Where it lives

pages/calculators/MortgagePayoffCalculator.tsx — page-local worker, input → result
engines/simulation/CFDEngine.worker.ts — framed request, transferable buffer
logic/*Worker.ts — Decimal arithmetic inside the worker

Output

results you can read and check

There are two output layouts, and the difference is structural rather than cosmetic. 241 pages return an EngineResult and let the shared shell render it: exactly four headline metrics, three status badges, one table, a chart stack, a diagnostics stack, the canonical equations, a notation panel and the computation steps. The other 131 pages lay their results out themselves.

What is identical across all 372 is the editorial layer beneath the live result: the formula as published, a worked example, at least 2 assumptions and at least 0 FAQs, loaded per slug. And in every layout the numbers are real DOM — selectable, copyable, readable by assistive technology and present in the prerendered HTML. Rounding happens only at the boundary; full precision stays inside the model.

Where it lives

components/engine-shell/EngineShell.tsx — metrics, table, charts, notation, steps
components/engine-shell/charts.tsx — SVG chart renderers
components/CalculatorContentSection.tsx — formula, example, assumptions, FAQs

Mount paths

One route, three ways to render it.

Every calculator is reachable at /engines/<slug>. The catch-all route resolves the slug against the static catalog and lazily loads the component named in that entry — but the component it loads is one of three kinds, and the difference decides what the page looks like.

241 calculators

Spec · shared shell

The page file is only a specification: inputs, a compute function, and the result it returns. defineEngine() hands that object to EngineShell, which renders the controls, the metrics, the table, the charts and the notation. Every page in this group therefore has the same output contract.

pages/calculators/*Engine.tsx → defineEngine(spec)

8 calculators

Bridge · engine chrome

A dedicated page wrapped in the engine chrome — a terminal, a tool panel and shared state. The page keeps its own layout; the wrapper adds commands and export. These are the calculators whose interaction model is a workspace rather than a form.

engines/<family>/<family>.engine.tsx

123 calculators

Standalone page

A bespoke component with its own layout, charts and interaction. It receives the same catalog entry and sits under the same editorial content layer, but it does not inherit the engine shell's result contract.

pages/calculators/*.tsx

Computational shapes

Seven ways a number gets made.

Every calculator in the catalog is one of these seven shapes. The shape decides how the page terminates, what it can promise about accuracy, and how much work it does per interaction. The registry at the bottom of this page assigns a primary shape to each of the 372 calculators and flags the 10 that run a second one.

01Direct

Count251

CostO(1) in inputs · O(N) in the sampling resolution where a sum or integral is tabulated.

Termination: Not applicable — no iteration, so no tolerance and no convergence failure.
Precision: Double throughout, unless the page imports Decimal.js or Big.js for currency.

Direct evaluation

one pass · no convergence

The answer is an algebraic function of the inputs, evaluated once.

The compute function normalises its inputs, substitutes them into the published relationship, and returns. No loop has to settle and no tolerance decides when to stop: the number of arithmetic operations is fixed by the formula, not by the data.

Finite sums count as direct evaluation. A bond price sums one discounted cash flow per coupon, a DFT sums N terms per bin, and the Heston price integrates the characteristic function on a fixed quadrature grid. Those loops are bounded by a resolution the page controls, so they terminate in a known number of steps and return the same answer every time.

NormaliseUnits to SI, percentages to fractions, select values narrowed to a union.
SubstituteEvaluate the relationship once — no state carried between iterations.
FormatFull precision stays in the number; rounding happens only in the formatter.

RepresentativeBlack-Scholes Options Calculator Bond Duration Calculator Ideal Gas Law Calculator WACC Calculator

02Schedule

Count57

CostO(n) in periods — 360 iterations for a 30-year monthly schedule.

Termination: A fixed number of periods, or the first period in which the balance reaches zero — the payoff pages test against a half-cent floor.
Precision: Decimal.js where the schedule must reconcile to the cent; doubles where it is a projection rather than a ledger.

Period schedule

carry the state forward

Each period's closing balance is the next period's opening balance.

Money-and-time models cannot collapse into one expression once a payment, a cap or a contribution rule depends on the balance. The page walks the calendar one period at a time, carrying a small state vector — balance, contributions to date, basis — and applying interest, payment and cap in a fixed order.

The order is the model. Interest accrues on the opening balance, the payment is applied to interest first and principal second, and a contribution cap is tested against the year-to-date total before it is added. Running the same inputs twice produces the same table, because nothing is sampled and nothing is rounded mid-schedule.

OpenRead the carried state: balance, year-to-date contributions, cost basis.
AccrueApply the period rate to the opening balance (or the cap to the contribution).
ApplyInterest first, then principal; extra payments go to the target balance.
ClampFloor the balance at zero so a final payment cannot overshoot into credit.
EmitPush the row, then carry the closing state into the next period.

RepresentativeAmortization Calculator Retirement Calculator Debt Snowball Calculator Depreciation Calculator

03Solve

Count21

CostO(iterations × cost of one residual evaluation).

Termination: IRR: bisection, 200 iterations, 1e-12 on NPV or on bracket width. Bond yield: Newton with bisection fallback, 80 iterations, bracket expanded ×1.5 up to 32 times. APR: 120 bisection passes on the monthly rate. Colebrook: 80 fixed-point passes at 1e-10 — the default pipe run converges in 7.
Precision: Double, with the residual compared against the scale of the quantity it measures.

Iterative solve

bracket, then converge

The answer is the input that drives a residual to zero.

Some quantities are defined implicitly: the rate that makes NPV zero, the yield that reproduces a market price, the friction factor that satisfies Colebrook, the eccentric anomaly that satisfies Kepler. Each page brackets the residual, then iterates inside the bracket.

Every solver here is bounded twice — by an iteration cap and by a tolerance — and reports the residual rather than only the root. Bisection halves the bracket and cannot diverge. Newton uses the analytic derivative when it has one and falls back to bisection the moment a step would leave the bracket, so a badly scaled input degrades the speed of convergence, not the answer.

BracketFind two points with opposite residual signs; expand the upper bound when needed.
IterateBisect, or take a Newton step from the current estimate.
GuardIf the step leaves the bracket or the derivative vanishes, bisect instead.
TestStop on |residual| below tolerance, or on the bracket width.
ReportReturn the root together with the residual that justifies it.

RepresentativeIRR Calculator Bond Yield Calculator Pipe Friction Loss Calculator Orbital Mechanics Calculator

04Simulate

Count10

CostO(paths × steps) — the heaviest shape in the catalog.

Termination: A fixed path count × step count. There is no convergence test, so the standard error is reported instead.
Precision: Double; the estimator carries its own sampling error and the page shows it.

Seeded simulation

same seed, same paths

A distribution is estimated by generating paths from a seeded generator.

Where the answer is a distribution rather than a number, the page generates samples: a uniform stream from mulberry32 or xorshift32, two uniforms combined by Box–Muller into a normal draw, and one step of the model per draw — an SDE step for a price path, a full round of a consensus protocol for a latency distribution, a whole retirement plan replayed under sampled returns, or a reliability integral estimated from sampled strength and load. The result is reduced to quantiles, tail statistics and an expected value.

The generator is seeded from an input, so a run is reproducible: the same inputs and the same seed produce the same path set, the same percentile and the same chart. That is what makes a simulated number auditable — you can regenerate it rather than take it on trust.

SeedInitialise the generator from the seed input, not from the clock.
DrawUniforms to normals by Box–Muller; independent draws per step.
StepAdvance the model: exact GBM step, Euler for local vol, or one simulated protocol round.
ReduceCollect terminal values, then take mean, quantiles and tail losses.
RegressLongstaff–Schwartz adds backward induction with a least-squares continuation value.

RepresentativeMonte Carlo Simulation Calculator American Option Calculator Value at Risk (VaR) Calculator Rough Volatility Calculator

05Matrix

Count18

CostO(n³) for a dense solve; the grid resolution is the dominant input.

Termination: Direct factorisation has no tolerance. The eigen solver sweeps rotations until the off-diagonal mass falls below its threshold.
Precision: Double — the conditioning of the matrix, not the formatter, sets the accuracy.

Matrix & eigen solve

assemble, then solve

The model is a linear system or an eigenproblem; the page assembles it and solves it.

Portfolio weights, nodal displacements and band structures share one shape: build a matrix from the inputs, then solve it. Markowitz and Black–Litterman invert a covariance; finite elements assemble a stiffness matrix and solve K u = f; buckling and photonic-band pages solve a generalised eigenproblem. The frame pages assemble a global stiffness from member contributions, and the load-flow page builds a Ybus and re-factorises its Jacobian on every Newton pass.

Assembly is where the physics lives, and it is where the page spends its code. Symmetry is preserved, pivoting is used so a zero pivot cannot silently corrupt the answer, and a singular system is surfaced as an error rather than returned as a plausible-looking vector.

AssembleBuild the matrix from element contributions, covariances or the plane-wave basis.
FactorLU or Gaussian elimination with pivoting; Jacobi rotations for a symmetric eigenproblem.
SolveBack-substitute for the field, weights or eigenvector.
DeriveTurn the solution into the reported quantities: stress, duration, band gap, risk contribution.
CheckResidual and conditioning checks; a singular matrix throws instead of returning zeros.

RepresentativePortfolio Optimization Calculator Black-Litterman Portfolio Calculator Finite Element Method (FEM) Calculator Photonic Band Structure Calculator

06Time march

Count12

CostO(steps × cells) — the second-heaviest shape after simulation.

Termination: A fixed step count derived from horizon ÷ dt; relaxation sweeps stop when the residual stops improving.
Precision: Double; the discretisation error dominates the floating-point error by orders of magnitude.

Time march

advance the state in steps

A PDE, a lattice or an incremental material law is advanced in time on a grid.

Transient heat conduction, re-entry heating, lattice-Boltzmann flow and Reynolds-averaged closure all evolve a field. The page discretises the domain, applies boundary conditions, and advances the state by a time step until the horizon is reached.

The scheme is chosen for stability, not speed. Diffusion is solved implicitly with a tridiagonal (Thomas) sweep, which stays stable at step sizes an explicit scheme would blow up on; the lattice-Boltzmann page collides and streams on a fixed lattice; the RANS page sweeps the domain until the residual stops falling. The step size is clamped and the page warns when the step is too coarse for the transient it is resolving.

DiscretiseBuild the grid or lattice; derive dt from the horizon and the resolution.
ConditionApply boundary conditions and the initial field.
StepImplicit tridiagonal solve, collide-and-stream, or a relaxation sweep.
UpdateCommit the new field and accumulate heat load, energy or residual history.
DiagnoseReport stability warnings when dt or the cell size under-resolves the physics.

RepresentativeHeat Transfer Calculator Hypersonic Reentry Heating Calculator Lattice Boltzmann Flow Calculator Navier-Stokes (RANS) Calculator

07Convert

Count3

CostO(1).

Termination: Not applicable — a fixed lookup and one arithmetic step.
Precision: Double; the factors are exact decimal literals, so error is one rounding per operation.

Table & conversion

lookup, then affine map

A discrete table supplies the factor; the conversion is one affine map.

Unit and code conversions are not physics, they are a table plus an affine map. Each unit carries a factor and an offset into a base unit, and a conversion is two multiplications and one subtraction — which is why temperature scales work through the same path as length.

The resistor page is the same shape with a discrete table in front: band colours map to digits and an exponent, then one multiplication produces the value and the tolerance band becomes an interval. Nothing is estimated, so the only failure mode is an unrecognised symbol.

ResolveMap the selected unit or colour band to its table entry.
To basex · factor + offset — one canonical unit for every dimension.
From base(base − offset) ÷ factor, so round trips are exact up to the double.
FormatApply the display precision after the conversion, never before.

RepresentativeUnit Converter Resistor Color Code Calculator

Worked traces

Two runs, followed all the way down.

A description of a method is a claim until it is run. These are the default inputs of two calculators, traced through their real compute paths — one schedule, one iterative solve — with every intermediate value the code produces.

Trace 01 · schedule

Auto loan · default inputs

price 32,000 · down 4,000 · trade-in 3,000 · tax 7% · fees 600 · APR 7.2% · 60 months

Quantity	Expression	Value
Taxable base	max(0, 32,000 − 3,000)	29,000.00
Sales tax	29,000 × 0.07	2,030.00
Amount financed	32,000 − 4,000 − 3,000 + 2,030 + 600	27,630.00
Monthly rate	0.072 ÷ 12	0.006
Payment	27,630 × 0.006 ÷ (1 − 1.006⁻⁶⁰)	549.72
Month 1 interest	27,630 × 0.006	165.78
Month 1 principal	549.72 − 165.78	383.94
Month 1 closing balance	27,630 − 383.94	27,246.06
Month 60 interest	balance before the last payment × 0.006	3.28
Total interest	549.72 × 60 − 27,630	5,353.08

The schedule runs on unrounded numbers and rounds only for display, which is why the final balance lands on exactly 0.00 rather than a few cents short. Source: AutoLoanFinancingEngine.tsx.

Trace 02 · solve

Pipe friction · Colebrook iteration

18 m³/h · DN50 · 60 m · ε 0.045 mm · ρ 998 kg/m³ · μ 1.002 mPa·s

A = 1.9635e−3 m²v = 2.5465 m/sRe = 126,815.7ε/D = 0.0009

Pass	f	\|Δf\|
1	0.02000000	1.42e−3
2	0.02141694	6.72e−5
3	0.02134978	3.04e−6
4	0.02135282	1.38e−7
5	0.02135268	6.27e−9
6	0.02135269	2.85e−10
7	0.02135269	1.29e−11

h_f = 8.472 mΔP = 82.91 kPatotal head +15% = 9.742 mpower = 0.477 kW

The solver seeds f at 0.02, runs fixed-point substitution, and stops when the change is below 1e-10 — seven passes here. The iteration cap is 80, so a pathological roughness degrades the answer to “best estimate after 80 passes” instead of hanging. Source: DarcyWeisbachPipeLossEngine.tsx.

Precision ledger

Where the accuracy actually comes from.

Precision is a property of the model, not a global setting. These counts are scanned from the imports and worker entry points of the calculators themselves.

360

work in IEEE-754 doubles

Measurement error dominates rounding error in physical models; the double is not the limiting term.

import Decimal.js

Currency and schedule arithmetic that must reconcile to the cent: amortisation, payoff, compound interest, mortgage.

route through Big.js

Both offload to a worker that keeps the ledger in exact decimal arithmetic.

seed a generator

Same inputs and same seed reproduce the same path set, percentile and chart.

spawn a Web Worker

The main thread never blocks on a schedule, a simulation or a field solve.

calculation endpoints

Every model is a function in the bundle. Nothing is posted anywhere to be computed.

Finance & markets

179 calculators

Payments & debtAnnuity-immediate payments, amortisation, extra-payment acceleration, HELOC draw and repayment, ARM resets, payoff ordering across balances.

Rates & bondsCompounding conventions, APY/EAR, yield-to-maturity, Macaulay and modified duration, convexity, bill discount, par-curve and caplet bootstrap.

Valuation & derivativesDiscounted cash flow with terminal value, IRR by bisection, NPV profiles, Black–Scholes, Heston, local volatility, autocallables, tranche pricing.

Risk & capitalCAPM, Sharpe/Sortino/Treynor, efficient frontier, VaR and expected shortfall, Kelly sizing, CVA/XVA, FRTB, IRRBB.

Tax & householdFederal and state brackets, capital gains with NIIT, estate and gift, RMD, Social Security claiming, 529 and HSA, rent versus buy.

Engineering & science

193 calculators

Units & structuresSection properties, beam deflection and shear, Euler and slender-column buckling, frame stiffness, seismic base shear, wind and snow load.

Fluids & heatReynolds and Colebrook friction factors, Darcy–Weisbach head loss, NPSH, LMTD and ε-NTU exchangers, steam and flash steam, psychrometrics.

Machines & electricalGear trains, spring rate, bearing life, welds, bolt torque, motor sizing, cable ampacity, conduit and box fill, arc flash, load flow.

Code checksACI 318 concrete, AISC 360 steel, TMS 402 masonry, ASCE 7 loads, NEC wiring, ASME B31.3 piping, API 520 relief, NDS timber.

Physics, numerics & statisticsOrbital mechanics, FEM assembly, lattice Boltzmann, Monte Carlo, design of experiments, ANOVA, process capability, reliability.

Registry · every calculator

The method behind all 372.

One row per calculator: the computational shape its compute path implements, the core relationship as published on its page, the source it is implemented against, the arithmetic it works in and how it is mounted. Filter by shape to see a method's full membership.

372 of 372 shown

Calculator	Shape	Core relationship	Arithmetic	Mount
Aeroacoustic Noise Calculatoraeroacoustic-turbulence-noise-engine	Direct	W=α ρ_0 (u'^(8))/(c_0^(5))L^(2), α≈38; ε=C_μ^(3/4)(k^(3/2))/(L), k= 32 u'^2; η=((ν^(3))/(ε))^(1/4); f_(peak)=0.2 (U)/(L) Proudman, "The generation of noise by isotropic turbulence," Proc. R. Soc. A 214 (1952); Lighthill, Proc. R. Soc. A 211 (1952); Pope, Turbulent Flows (2000), ch. 6 (Kolmogorov scales); ISO 9613-2:1996 (atmospheric attenuation).	Decimal.js	Engine bridge
Aeroelastic Flutter Calculatornonlinear-aeroelastic-flutter-boundary-engine	Solve+ Matrix	M q + C q + Kq = F_(aero)(q, q), det(A - λ I) = 0, flutter at ℜ(λ) = 0 Theodorsen (1935) unsteady aerodynamics; Dowell et al., "A Modern Course in Aeroelasticity".	Double	Dedicated
Airfoil Lift & Drag Calculatoraerodynamic-airfoil-lift-drag-matrix	Direct	α_(L0) = -(1)/(π)∫_0^(π)(dz)/(dx) (cosθ_0 - 1) dθ_0, C_l = 2π (α - α_(L0)) Thin-airfoil theory: Anderson, Fundamentals of Aerodynamics (6th ed.), Ch. 4; zero-lift angles tabulated in Abbott & von Doenhoff, Theory of Wing Sections.	Decimal.js	Dedicated
Anchor Bolt Calculatoranchor-bolt-calculator	Direct	N_(cb) = (A_(Nc))/(A_(Nco)) ψ_(ed,N) 24λ√(f'_c) h_(ef)^(1.5) ACI 318-19 Chapter 17, §17.6.1 (steel), §17.6.2 (breakout) and §17.6.3 (pullout).	Double	Engine shell
Angle and Channel Propertiesangle-channel-properties	Direct	— Centroidal properties for angle and channel sections.	Double	Dedicated
ANOVA Calculatoranova-calculator	Direct	F = (MS_(between))/(MS_(within)), η^2 = (SS_(between))/(SS_(total)) One-way analysis of variance; F distribution with (k−1, N−k) degrees of freedom.	Double	Engine shell
Arc Flash Calculatorarc-flash-calculator	Direct	E = 4.184 C_f E_n ((t)/(0.2))((610)/(D))^(x) IEEE 1584-2002, Guide for Performing Arc-Flash Hazard Calculations; NFPA 70E for the PPE categories.	Double	Engine shell
AS 3600 Concrete Shearas3600-concrete-check	Direct	— AS 3600 cl. 8.2.4.1 concrete shear with the β1 size effect.	Double	Dedicated
ASCE 7 Wind Load Calculatorasce-wind-load-calculator	Direct	q_z = 0.613 K_z K_(zt) K_d V^2, p = q_z G C_p - q_z GC_(pi) ASCE 7-22 Chapter 26 (velocity pressure) and Chapter 27 (main wind-force-resisting system).	Double	Engine shell
ASME Pipe Thickness Calculatorasme-pipe-thickness-calculator	Direct	t = (P D)/(2 (S E W + P Y)) + c ASME B31.3 Process Piping, §304.1.2 (straight pipe under internal pressure).	Double	Engine shell
Bandwidth & Data Throughput Calculatordata-throughput-bandwidth-core	Direct	C = B log_2 (1 + SNR), FSPL(dB) = 32.44 + 20log_(10) f_(MHz) + 20log_(10) d_(km), N_(dBm) = -174 + 10log_(10) B + NF Shannon-Hartley channel-capacity theorem (Shannon, 1948); free-space path loss per ITU-R P.525; thermal-noise floor −10·log₁₀(kT₀) = −174 dBm/Hz at T₀ = 290 K (Boltzmann constant, Johnson-Nyquist noise).	Decimal.js	Dedicated
Base Plate Calculatorbase-plate-calculator	Direct	A_1 = (P_u)/(0.65 × 0.85 f'_c √(A_2/A_1)) AISC 360 §J8 for bearing; AISC Design Guide 1 for the plate thickness.	Double	Engine shell
Base Plate Designbase-plate-design	Direct	— AISC DG1 cantilever model for a concentrically loaded base plate.	Double	Dedicated
Battery Runtime Calculatorbattery-runtime-calculator	Direct	t = (C_(20)((C_(20))/(20I))^(k-1)DoD f_T f_a)/(I) Peukert's equation (1897); depth, temperature and age derating follow IEEE 485 battery-sizing practice.	Double	Engine shell
Beam Deflection & Stress Calculatorbeam-deflection-calculator	Matrix	EI(d^4w)/(dx^4) = q(x), δ_(max) = (5wL^4)/(384EI) (simply supported, UDL), M = EI(d^2w)/(dx^2) Timoshenko beam theory; Gere & Goodno, "Mechanics of Materials"; AISC 360 serviceability provisions.	Double	Dedicated
Beam Shear Calculatorbeam-shear-calculator	Direct	φ V_n = 0.75(V_c+V_s), V_s=A_v f_y d/s; V_c= cases(0.17λ√(f'_c)+N_u/6A_g)b_wd,&A_v≥ A_(v,min)\(0.66λ_sλρ_w^(1/3)√(f'_c)+N_u/6A_g)b_wd,&A_v<A_(v,min) cases ACI 318-19 / 318-19(22) Table 22.5.5.1 and §§22.5.5, 22.5.10, 9.6.3 and 9.7.6; λs per Table 22.5.5.1.3.	Double	Engine shell
Bearing Life Calculatorbearing-life-calculator	Direct	L_(10) = ((C)/(P))^p, L_(10h) = (L_(10) · 10^6)/(60n) ISO 281:2007 rolling bearing rating life; a1 reliability factors.	Double	Engine shell
Bolt Torque Calculatorbolt-torque-calculator	Direct	T = K F d; A_t = (π)/(4)(d - (0.9743)/(n))^2 RCSC Specification for Structural Joints, Table J3.1 for minimum pretension and §8.2 for turn-of-nut; AISC 360 Table J3.2 for tensile strength.	Double	Engine shell
Box Fill Calculatorbox-fill-calculator	Direct	V = (n_u + n_g)A + A + 2dA + cA + fA NFPA 70 §314.16, Table 314.16(A) for box volumes and Table 314.16(B) for the conductor allowance.	Double	Engine shell
Brayton Cycle Calculatorbrayton-cycle-calculator	Direct	η_(ideal) = 1 - (1)/(r_p^((k-1)/k)) Cold-air-standard Brayton analysis; the isentropic relations and the efficiency definitions are standard.	Double	Engine shell
Bridge Load Ratingbridge-load-rating	Direct	— AASHTO MBE load rating: RF = (φRn − γDC·DC − γDW·DW)/(γLL(LL+IM)).	Double	Dedicated
Building Energy Estimatebuilding-energy-model	Direct	E = (UA HDD 24)/(1000 η)(1-g) + (UA CDD 24)/(1000 COP)(1+g) ASHRAE Fundamentals, degree-day method.	Double	Dedicated
Cable Ampacity Calculatorcable-ampacity-calculator	Direct	I_(allow)=min(I_(table)f_(temp)f_(conductors),I_(terminal)); I_(design)=1.25I_(continuous); I_(design)≤ I_(OCPD)≤min(I_(allow),I_(240.4(D))) NFPA 70 (NEC) Tables 310.16, 310.15(B)(1), 310.15(C)(1), §§110.14(C), 210.19(A)(1), 240.4(D); resistance from Chapter 9, Table 8.	Double	Engine shell
Cable Pulling Tensioncable-pulling-tension	Direct	— Capstan equation through bends; sidewall pressure at the radius.	Double	Dedicated
Chiller Plant Sizingchiller-plant-sizing	Direct	— Tons, COP and kW/ton conversions.	Double	Dedicated
Coil Geometry Calculatorcoil-geometry-calculator	Direct	A = V / v_(face); f = 0.316 Re^(-0.25); Δ p_w = (f(L)/(d_i) + Σ K)(ρ v^2)/(2) Darcy–Weisbach with the Blasius friction factor; air-side correlation calibrated to published finned-coil curves.	Double	Engine shell
Cold-Formed Steel Checkcold-formed-steel-check	Direct	— AISI S100 §E2 with φc = 0.85.	Double	Dedicated
Column Buckling Calculatoreuler-bernoulli-column-buckling-matrix	Matrix	P_(cr) = (π^(2) E I)/((K L)^(2)), r = (I)/(A), λ = (K L)/(r), σ_(cr) = (P_(cr))/(A) Euler elastic buckling of a prismatic column; Timoshenko & Gere, Theory of Elastic Stability; effective-length factors K per standard end-condition cases (e.g. AISC Table C-A-7.1).	Double	Dedicated
Column Interaction Diagramcolumn-interaction-diagram	Direct	P_n, M_n from a sweep of c, (1)/(P_n) = (1)/(P_(nx)) + (1)/(P_(ny)) - (1)/(P_0) ACI 318-19 §22.2 (stress block), Table 21.2.2 (φ transition), Bresler reciprocal load method.	Double	Engine shell
Compressible Flow & Shock Wave Calculatorcompressible-flow-isentropic-shock-wave-engine	Solve+ Direct	(T_0)/(T)=1+(γ-1)/(2)M^2, M_2^2=(1+(γ-1)/(2)M_1^2)/(γ M_1^2-(γ-1)/(2)), (p_2)/(p_1)=1+(2γ)/(γ+1)(M_1^2-1) NACA Report 1135, "Equations, Tables, and Charts for Compressible Flow" (Ames Research Staff, 1953); Anderson, Modern Compressible Flow, 3rd ed., chs. 3-4.	Decimal.js	Dedicated
Computational Fluid Dynamics Calculatorcomputational-fluid-dynamics-solver	Solveworker	Re=(ρ V D)/(μ), (1)/(√(f))=-2log_(10) ((ε/D)/(3.7)+(2.51)/(Re√(f))), h_f=f(L)/(D)(V^2)/(2g), Δ p=ρ g h_f Colebrook, J. Inst. Civ. Eng. 11 (1939); Darcy-Weisbach equation as given in White, Fluid Mechanics, 7th ed., ch. 6; Moody, Trans. ASME 66 (1944).	Decimal.js	Engine bridge
Concrete Anchor Designanchor-design-concrete	Direct	N_(cb) = (A_(Nc))/(A_(Nco))ψ_(ed) N_b, N_b = 10λ_a√(f'_c) h_(ef)^(1.5) ACI 318-19 §17.6.2 (breakout), §17.6.3 (pullout), §17.7 (shear), φ = 0.70.	Double	Engine shell
Concrete Beam Design Calculatorconcrete-beam-design-calculator	Direct	a = (A_s f_y)/(0.85 f'_c b), φ M_n = φ A_s f_y (d - (a)/(2)) ACI 318-19 §22.2 (equivalent rectangular stress block), §9.6.1.2 (minimum steel), §21.2 (tension control).	Double	Engine shell
Concrete Calculatorconcrete-calculator	Direct	V = L W T (1+w); c = (w)/(w/c); 27 = V_w + V_c + V_(air) + V_(fa) + V_(ca) ACI 211.1, Standard Practice for Selecting Proportions for Normal, Heavyweight and Mass Concrete, Tables 6.3.3, 6.3.4 and 6.3.6.	Double	Engine shell
Concrete Column Calculatorconcrete-column-calculator	Direct	φ P_(n,max) = 0.65 · 0.80 [0.85 f'_c (A_g - A_(st)) + f_y A_(st)] ACI 318-19 §22.4.2 (tied columns), §10.6.1.1 (steel limits), §6.2.5 (slenderness).	Double	Engine shell
Concrete Torsion Checkconcrete-torsion-calculator	Direct	— ACI 318 §22.7.4.1 torsion threshold.	Double	Dedicated
Conduit Fill Calculatorconduit-fill-calculator	Direct	fill = (n × A_(cond))/(A_(raceway)) ≤ 0.40 NFPA 70 Chapter 9 Table 1 (allowance), Table 4 (raceway area) and Table 5 (conductor area); the nipple exception is §310.14(A)(2).	Double	Engine shell
Confidence Interval Calculatorconfidence-interval-calculator	Direct	x ± z (σ)/(√(n)) Normal approximation to the sampling distribution of the mean.	Double	Engine shell
Consolidation Settlement Calculatorfem-settlement	Direct	s = (C_c H)/(1+e_0)log_(10) ((σ'_0+Δσ)/(σ'_0)) Terzaghi one-dimensional consolidation; ASTM D2435 for Cc and cv.	Double	Dedicated
Control Valve Calculatorcontrol-valve-calculator	Direct	C_v = Q (G_f)/(Δ P); Δ P_(ch) = F_L^2(P_1 - F_f P_v); Q = 1360 C_v P_1 Y (x)/(G_g T Z) IEC 60534-2-1 and ISA-75.01.01; recovery factor and terminal ratio from the valve manufacturer's data sheet.	Double	Engine shell
Convection Calculatorconvection-calculator	Direct	h = (Nu k)/(L) Blasius and Colburn for the plate, Dittus-Boelter for the pipe, Churchill-Chu for the vertical plate.	Double	Engine shell
Cooling Coil Selection Calculatorcoil-selection-calculator	Direct	ADP = t_w + Δ t_(app); BF = (t_2 - ADP)/(t_1 - ADP); Q = m_(da)(h_1 - h_2) ASHRAE Handbook — Fundamentals, psychrometrics and cooling-coil apparatus dew point; Carrier psychrometric chart construction.	Double	Engine shell
Cooling Load Calculatorcooling-load-calculator	Direct	Q_s = 1.2 Q c_p Δ T, Q_l = 1.2 Q Δ W 2501 ASHRAE psychrometrics; Magnus formula for saturation pressure.	Double	Engine shell
Cooling Tower and Chiller Plantcooling-tower-sizing	Direct	E = (Q)/(h_(fg)), B = (E)/(COC - 1) Latent heat of vaporisation at about 2,450 kJ/kg; blowdown from the cycles of concentration.	Double	Engine shell
Crane Load Calculatorcrane-load-calculator	Direct	— ASCE 7 §4.9 lateral force; impact factor on the vertical.	Double	Dedicated
CSA S16 Steel Checkcsa-steel-check	Direct	— CSA S16 cl. 13.3.1 compression and cl. 13.2 tension, φ = 0.90.	Double	Dedicated
Daylighting Calculatordaylighting-calculator	Direct	— Split-flux daylight factor, BRE guidance.	Double	Dedicated
Decibel Calculatordecibel-calculator	Direct	L = 10log_(10)(P)/(P_0), L = 20log_(10)(A)/(A_0), L_(Σ) = 10log_(10) (10^(L_1/10) + 10^(L_2/10)), Δ L = -20log_(10)(r_2)/(r_1) IEC 60027-3 (logarithmic quantities); ISO 9613-1 for atmospheric attenuation.	Double	Engine shell
Discrete Fourier Transform (DFT) Calculatordiscrete-fourier-transform-signal-matrix	Direct	X[k] = Σ_(n=0)^(N-1) x[n] e^(-j 2π k n / N), x[n] = (1)/(N)Σ_(k=0)^(N-1) X[k] e^(+j 2π k n / N), Σ_(n=0)^(N-1) \|x[n]\|^(2) = (1)/(N)Σ_(k=0)^(N-1) \|X[k]\|^(2) Oppenheim & Schafer, Discrete-Time Signal Processing (DFT, Parseval's relation); Cooley–Tukey radix-2 FFT (Math. Comp. 19, 1965); window definitions from Harris, "On the use of windows", Proc. IEEE 66 (1978).	Double	Dedicated
Distillation Calculatordistillation-calculator	Solve	N_(min) = (ln[(x_D)/(1-x_D)·(1-x_B)/(x_B)])/(lnα) Fenske (1932), Underwood (1948), Gilliland (1940); the Eduljee (1975) fit to the Gilliland correlation.	Double	Engine shell
Duct Fitting Lossesduct-fitting-losses	Direct	— Δp = K·0.5·ρ·V²; K from ASHRAE fitting tables.	Double	Dedicated
Duct Network Calculatorduct-network-calculator	Direct	Δ p = Σ ( f (L)/(D) + Σ K ) (ρ v^2)/(2) Darcy–Weisbach friction plus local loss coefficients; standard duct design practice.	Double	Engine shell
Duct Sizing Calculatorduct-sizing-calculator	Direct	D = √(4Q/(π v)), Δ p = f (L)/(D) (ρ v^2)/(2) Darcy–Weisbach with the Swamee-Jain approximation to Colebrook–White.	Double	Engine shell
Eccentric Bolt Groupbolt-group-eccentric	Direct	f_d = (P)/(n), f_t = (M r)/(Σ(x^2 + y^2)), f = (f_(dx)+f_(tx))^2 + (f_(dy)+f_(ty))^2 AISC Manual Part 7, elastic method (conservative against the instantaneous centre method).	Double	Engine shell
Economiser Saving Calculatoreconomiser-calculator	Direct	E_(net) = (Q · h)/(COP) - P_(fan) · h ASHRAE air-side economiser analysis; screening estimate.	Double	Engine shell
Elastoplastic Damage Calculatornonlinear-elastoplastic-damage-core	Time march	ε = ε^e + ε^p, σ = E(ε - ε^p), f = \| σ\| - (σ_(y0) + Hα) ≤ 0, Δγ = (f_(trial))/(E + H), σ = (1 - D) σ Small-strain J2 (von Mises) plasticity with linear isotropic hardening and scalar (Lemaitre-type) damage; Simo & Hughes, Computational Inelasticity (radial return); Lemaitre, A Course on Damage Mechanics; ZSoil CPDM manual (combined damage D = 1−(1−D_c)(1−sD_t)); GetFEM small-strain plasticity notes.	Double	Dedicated
Elliptic Curve Cryptography Calculatorcryptographic-elliptic-curve-scalar-field-engine	Direct	Q = dG, λ = (y_2 - y_1)/(x_2 - x_1), x_3 = λ^(2) - x_1 - x_2, y_3 = λ(x_1 - x_3) - y_1 p, y^(2) ≡ x^(3) + ax + b p SEC 1: Elliptic Curve Cryptography (Certicom, v2.0) short-Weierstrass group law and double-and-add scalar multiplication; NIST SP 800-186; secp256k1 parameters from SEC 2.	Double	Dedicated
Eurocode 3 Steel Checkeurocode-steel-check	Direct	N_(b,Rd) = (χ A f_y)/(γ_(M1)), χ = (1)/( + √( ^2 - λ^2)) EN 1993-1-1 §6.2 and §6.3.1, γM0 = γM1 = 1.0.	Double	Engine shell
Fan Curve Calculatorfan-curve-calculator	Direct	Q = √(a/(K + b)), Q ∝ n, Δ p ∝ n^2, P ∝ n^3 Fan affinity laws; backward-curved centrifugal curve approximation.	Double	Engine shell
Fatigue Life Calculatorfatigue-life-calculator	Direct	S_e = k_a k_b k_c (0.5 S_u); S_f = a N^b; D = Σ (n_i)/(N_i) Shigley's Mechanical Engineering Design, §6-9 to §6-12 for the Marin factors and the S-N construction; ASTM E739 for the stress-life method.	Double	Engine shell
Fillet Weld Calculatorfillet-weld-calculator	Direct	R_n = 0.60 F_(EXX) (0.707 w) l AISC 360 §J2.4 for fillet weld strength, Table J2.4 for minimum size and §J2.2b for maximum size.	Double	Engine shell
Fin Efficiency Calculatorfin-efficiency-calculator	Direct	η_f = (tanh(mL_c))/(mL_c), m = (2h)/(kt) The hyperbolic solution for a straight rectangular fin with a convective tip (Incropera & DeWitt).	Double	Engine shell
Finite Element Method (FEM) Calculatorfinite-element-method-mesh-solver	Matrix	ε = Bu, σ = D ε, K_e = t A B^ TDB, KU = F, σ_(vM) = σ_x^2 - σ_xσ_y + σ_y^2 + 3τ_(xy)^2 Constant-strain triangle (CST) plane-elasticity formulation and global assembly K_e = t A Bᵀ D B, K U = F; Zienkiewicz, Taylor & Zhu, The Finite Element Method; Cook, Malkus, Plesha & Witt, Concepts and Applications of Finite Element Analysis; Logan, A First Course in the Finite Element Method.	Double	Dedicated
Finite Element Stress Calculatorfinite-element-stress-tensor-solver	Matrix	ε = Bu, σ = D ε, K_e = t A B^( )DB, σ_(vM) = σ_(xx)^2 - σ_(xx)σ_(yy) + σ_(yy)^2 + 3τ_(xy)^2 Constant-strain triangle plane elasticity and the finite-element patch test; Zienkiewicz & Taylor, The Finite Element Method; Cook, Malkus & Plesha, Concepts and Applications of Finite Element Analysis; MIT OCW / solidmechanics.org linear-elasticity notes.	Double	Dedicated
Flange Rating (ASME B16.5)flange-rating-calculator	Schedule	P_(allow) = f(class,material,T) ASME B16.5 Table 2, carbon steel and austenitic stainless groups.	Double	Dedicated
Flash Steam Calculatorflash-steam-calculator	Direct	x = (h_(f1) - h_(f2))/(h_(fg2)) Energy balance across the trap; saturated properties from IAPWS-IF97.	Double	Engine shell
Flashing Control Valve Calculatorflashing-valve-calculator	Solve	C_v = (Q)/(F_L√((P_1 - F_F P_v)/G)) IEC 60534-2-1, industrial-process control valves, sizing equations for incompressible fluid flow.	Double	Engine shell
Floor Vibration Checkvibration-serviceability	Direct	— AISC Design Guide 11 frequency criterion.	Double	Dedicated
Footing Design Calculatorfooting-design-calculator	Direct	A = (1.1P)/(q_a); V_u = P_u - q_u(c+d)^2 ACI 318-19 for one-way shear (§22.5), two-way shear (§22.6), flexure and the shrinkage minimum; allowable bearing is a geotechnical input.	Double	Engine shell
Fractional Factorial Calculatorfractional-factorial-calculator	Directseeded	I = ABCD; e = (2)/(n)Σ_i x_i y_i; R = min \|w\| Box, Hunter & Hunter, Statistics for Experimenters, ch. 12 (fractional factorials, resolution and blocking).	Double	Engine shell
Fracture Mechanics Calculatorfracture-mechanics-calculator	Direct	K_I = Y σ√(π a); K_r = (K_I)/(K_(mat)); L_r = (σ)/(σ_Y) BS 7910:2019, Guide to methods for assessing the acceptability of flaws in metallic structures, Option 1.	Double	Engine shell
Frame Analysis Calculatorframe-analysis-calculator	Matrix	K_e u = F; (K_e - K_g)u = F; det(K_e - λ K_g) = 0 Direct stiffness method for 2D frames; consistent geometric stiffness (Cook et al., Concepts and Applications of Finite Element Analysis, ch. 11).	Double	Engine shell
Frame Load Combinations Calculatorframe-combinations-calculator	Matrix	q_z = 0.613 K_z K_(zt) K_d V^2; C_s = (S_(DS))/(R/I_e); 1.2D + 1.0E + L ASCE 7-22 §26.10 (velocity pressure), §12.8.1.1 (base shear) and §2.3.1 (strength combinations).	Double	Engine shell
Frame Model Calculatorframe-model-calculator	Matrix	node x y [support]; member i j [w=] [mass=] [P=@]; (K_e - K_g)φ = ω^2 Mφ Direct stiffness method; Guyan reduction of massless rotations; Jacobi eigensolver for the generalised problem.	Double	Engine shell
Gas Radiation Calculatorgas-radiation-calculator	Direct	ε_g = Σ_i a_i(T) (1 - e^(-b_i pL)) Three-term weighted-sum-of-gray-gases fit; flux in the Hottel form.	Double	Engine shell
Gear Ratio Calculatorgear-ratio-calculator	Direct	i = (N_(driven))/(N_(driver)), i_(total) = i_1 i_2, ω_(out) = (ω_(in))/(i_(total)), T_(out) = T_(in) i_(total) η^(n) Standard involute spur-gear kinematics; AGMA 2001 for load ratings.	Double	Engine shell
Grounding Conductor Calculatorgrounding-conductor-calculator	Direct	GEC = min (Table 250.66, electrode cap ) NFPA 70 Table 250.66, Table 250.122, §250.66(A) to (C).	Double	Engine shell
Grounding Grid Calculatorgrounding-grid-design	Direct	E_(touch) = (1000 + 1.5 C_s ρ_s)(0.116)/(√(t_s)) IEEE 80 §8 step and touch criteria; simplified Schwarz grid resistance.	Double	Engine shell
Harmonic Analysisharmonic-analysis	Direct	— THD and the K-factor transformer rating.	Double	Dedicated
Heat Conduction Calculatorheat-conduction-calculator	Direct	Q = (kAΔ T)/(L), R = (L)/(kA), q'' = (Q)/(A), U = (1)/(RA), T_i = T_(hot) - QR_1 Incropera & DeWitt, "Fundamentals of Heat and Mass Transfer", ch. 3; ISO 6946 for building U-values.	Double	Engine shell
Heat Exchanger Calculatorheat-exchanger-calculator	Direct	Q = mc_pΔ T, LMTD = (Δ T_1-Δ T_2)/(ln(Δ T_1/Δ T_2)), NTU = (UA)/(C_(min)), ε = (Q)/(Q_(max)) Incropera & DeWitt, "Fundamentals of Heat and Mass Transfer", ch. 11.	Double	Engine shell
Heat Loss Calculatorheat-loss-calculator	Direct	Q = U A Δ T + 0.33 ACH V Δ T CIBSE and ASHRAE steady-state heating load method.	Double	Engine shell
Heat Transfer Calculatorradiative-conjugate-heat-transfer-matrix	Time march	ρ c_p(∂ T)/(∂ t) = (∂)/(∂ x) (k(∂ T)/(∂ x)), q^( )_(conv) = h (T_g - T_s), q^( )_(rad) = εσ (T_(env)^(4)-T_s^(4)), J_i = ε_iσ T_i^(4) + (1-ε_i)Σ_j F_(ij)J_j Stefan-Boltzmann radiative exchange and the gray-enclosure radiosity method (Incropera & DeWitt, Fundamentals of Heat and Mass Transfer; Modest, Radiative Heat Transfer). 1D transient conduction discretized in conservative finite-volume form with implicit Euler; σ = 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴ (CODATA/NIST).	Double	Dedicated
HSS Section Propertieshss-section-properties	Direct	— Section properties from geometry; closed-section torsion.	Double	Dedicated
Hydraulic Cylinder Calculatorhydraulic-cylinder-force-calculator	Direct	A_b = (π d_b^2)/(4), A_a = (π (d_b^2 - d_r^2))/(4), F = p A η, v = (Q)/(A) Pascal's principle and continuity; ISO 4413 hydraulic fluid power — general rules and safety requirements.	Double	Engine shell
Hypersonic Reentry Heating Calculatorhypersonic-reentry-thermal-protection-solver	Time march	q_c = C (ρ_∞)/(R_n) V_∞^(3), ρ c_p (∂ T)/(∂ t) = (∂)/(∂ x) (k (∂ T)/(∂ x)), -k(∂ T)/(∂ x) \|_(s) = q_c - εσ (T_s^(4)-T_(ref)^(4)) Sutton & Graves, “A General Stagnation-Point Convective-Heating Equation for Arbitrary Gas Mixtures,” NASA TR R-376 (1971); 1D transient conduction solved by implicit finite-volume marching as in NASA NTRS TPS thermal-response analyses. Earth-air coefficient C ≈ 1.83×10⁻⁴ (SI).	Double	Dedicated
Ideal Gas Law Calculatorideal-gas-law-calculator	Direct	PV = nRT, n = (PV)/(RT), ρ = (PM)/(RT), R = 8.314462618 J/(mol·K) ISO 80000-5; CODATA 2018 value of the molar gas constant.	Double	Engine shell
Insulation Thickness Calculatorinsulation-thickness-calculator	Direct	q = (Δ T)/((ln(r_2/r_1))/(2π k) + (1)/(2π r_2 h)) Cylindrical conduction with a surface film coefficient, ASTM C680 and ISO 12241 practice.	Double	Engine shell
Lateral Pile Analysislateral-pile-analysis	Direct	— Hetényi beam on an elastic foundation; long-pile closed form.	Double	Dedicated
Lattice Boltzmann Flow Calculatorlattice-boltzmann-mesoscopic-flow-core	Time march	ν=c_s^2(τ- 12), c_s^2= 13; f_i^(eq)=w_iρ[1+(e_i )/(c_s^2)+((e_i )^2)/(2c_s^4)-(u )/(2c_s^2)]; E(t)=E_0 e^(-2ν k^2 t) Kruger et al., The Lattice Boltzmann Method: Principles and Practice (Springer, 2017); Bhatnagar, Gross & Krook, Phys. Rev. 94 (1954); Taylor & Green, Proc. R. Soc. A 158 (1937).	Double	Dedicated
Layered Slope Stability Calculatorlayered-slope-stability-calculator	Solve	F = (Σ [c b + (W - ub)tanφ]/n_α)/(Σ W tanα) Janbu simplified method with the f₀ correction (Janbu 1973), on a non-circular surface.	Double	Engine shell
Lighting Calculatorlighting-calculator	Direct	RCR = (5h(L+W))/(LW); N = (E A)/( CU LLF) IES Lighting Handbook, lumen method; the cavity-ratio definition and the CU tables are in IES LM-57 and the IES Fundamentals volume.	Double	Engine shell
Liquefaction Assessmentliquefaction-assessment	Direct	— Seed–Idriss simplified CSR with the CRR curve for (N1)60cs.	Double	Dedicated
Masonry Wall Calculatormasonry-wall-calculator	Direct	(f_a)/(F_a) + (f_b)/(F_b) ≤ 1 TMS 402-16 §8.3.4 for axial compression and §8.3.3 for flexural compression, allowable-stress design.	Double	Engine shell
Mat Foundation (Rigid Method)mat-foundation-fem	Direct	q = (P)/(A) ± (M_x)/(S_x) ± (M_y)/(S_y) ACI 336.2R rigid-mat method; ACI 318 §22.6 punching shear.	Double	Dedicated
Motor FLA Calculatormotor-fla-calculator	Direct	I_(cond) = 1.25 I_(FLA); I_(prot) = k I_(FLA) NFPA 70 Article 430: Table 430.250 and 430.248 for FLA, §430.22, §430.32, §430.52 and §430.83.	Double	Engine shell
Motor Sizing Calculatormotor-sizing-calculator	Direct	T_(peak) = T_(load) + Jα, P = (Tω)/(η) Newton’s second law for rotation; standard servo and induction motor sizing practice.	Double	Engine shell
Motor Starting Voltage Dipmotor-starting-calculator	Direct	— IEEE 399 (Brown Book) motor-starting voltage dip: dip ≈ kVA_start / (kVA_fault + kVA_start), with NEMA MG 1 locked-rotor current.	Double	Dedicated
Navier-Stokes (RANS) Calculatornavier-stokes-reynolds-averaged-closure-core	Time march	u_j ∂ u_i∂ x_j = -(1)/(ρ) ∂ p∂ x_i + ν∇^2 u_i - ∂ u_i'u_j'∂ x_j, u^+ = (1)/(κ)ln y^+ + A^+ Reynolds (1895) averaging; Launder & Spalding (1974) wall-function treatment.	Double	Dedicated
Network Latency Calculatordistributed-consensus-network-latency-solver	Simulate+ Directseeded	q = N/2 + 1, A_(quorum) = Σ_(j=q)^(N) Nj p^( j)(1-p)^( N-j), ρ = (λ)/(μ), W_q = (ρ)/(μ-λ) Raft majority-commit and timing rules (Ongaro & Ousterhout, “In Search of an Understandable Consensus Algorithm,” 2014); Paxos prepare/accept phases (Lamport, “Paxos Made Simple,” 2001); binomial quorum availability; M/M/1 queue mean wait W_q = ρ/(μ−λ) (Kleinrock, Queueing Systems).	Double	Dedicated
NPSH Calculatornpsh-calculator	Direct	NPSH_a = (p_(atm) - p_v)/(ρ g) + z - h_f Hydraulic Institute standards for rotodynamic pumps; standard cavitation margin practice.	Double	Engine shell
OEE Calculatoroee-calculator	Direct	OEE = A × P × Q Total productive maintenance (Nakajima) definition of OEE.	Double	Engine shell
Ohm's Law Calculatorohms-law-calculator	Direct	V = IR, P = VI = I^2R = (V^2)/(R), cost = (P t)/(1000)× tariff Ohm's law; Joule's law; standard DC circuit analysis.	Double	Dedicated
Open Channel Flow Calculatoropen-channel-flow-calculator	Solve	Q = (1)/(n) A R^(2/3) S^(1/2) Manning's equation; roughness values from Chow, Open-Channel Hydraulics, and FHWA HDS-3.	Double	Engine shell
Optimal Design Calculatoroptimal-design-calculator	Directseeded	max \|X'X\|; D-eff = (\|X'X\|^(1/p))/(n); Var( y) = σ^2 x'(X'X)^(-1)x Coordinate exchange (Meyer & Nachtsheim, 1995); Scheffé mixture models (Scheffé, 1958).	Double	Engine shell
Optional Method Service Load Calculatorservice-load-optional-calculator	Direct	L = min(G, 10,000) + 0.4 (G - 10,000) + L_(HVAC) NFPA 70 §220.82, optional feeder and service load calculations.	Double	Engine shell
Orbital Mechanics Calculatororbital-mechanics-keplerian-state-engine	Solve	M = E - esin E, r = (a(1-e^(2)))/(1+ecosν), v = μ((2)/(r)-(1)/(a)), T = 2π (a^(3))/(μ) Classical two-body orbital mechanics: Kepler’s equation and the vis-viva (energy) integral. Vallado, Fundamentals of Astrodynamics and Applications; Curtis, Orbital Mechanics for Engineering Students.	Double	Dedicated
Orifice Flow Calculatororifice-flow-calculator	Direct	Q = C_d A (2Δ P)/(ρ); m = C_d A P_1 (k)/(RT)((2)/(k+1))^(k+1)/(2(k-1)) ISO 5167 for orifice plates; the compressible-flow expression is the isentropic choked-nozzle result from Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow.	Double	Engine shell
Photonic Band Structure Calculatorphotonic-crystal-band-structure-solver	Matrix	Σ_(G') (k+G)·(k+G') ε^(-1)_(G-G') H_(G') = ((ω)/(c))^(2) H_(G), ω = (ω a)/(2π c) Plane-wave expansion of the Maxwell eigenproblem in periodic dielectrics; Johnson & Joannopoulos, Opt. Express 8 (2001); Busch et al., C. R. Physique 3 (2002). Empty-lattice (free-photon) band folding used as the analytic validation case.	Double	Dedicated
PID Tuning Calculatorpid-tuning-calculator	Direct	K_c = 1.2 (τ)/(Kθ); T_i = 2θ; T_d = 0.5θ Ziegler & Nichols (1942); Cohen & Coon (1953); Rivera, Morari & Skogestad (1986) for IMC.	Double	Engine shell
Pile Cap Designpile-cap-design	Direct	— ACI 318 §22.6 punching at d/2 from the column face.	Double	Dedicated
Pile Capacity Calculatorpile-capacity-calculator	Direct	Q_(ult) = q_p A_p + f_s π D L Meyerhof (1976) as summarised in FHWA deep-foundation design guidance.	Double	Engine shell
Pile Group Calculatorpile-group-calculator	Direct	E_g = 1 - (θ[(n-1)m + (m-1)n])/(90 mn) Converse-Labarre for group efficiency; undrained block failure from the group perimeter and base.	Double	Engine shell
Pile Settlement Calculatorpile-settlement-calculator	Direct	s = (q B (1 - ν^2) I)/(E_s) + (Q L)/(2 A E_p) Equivalent raft method (Tomlinson), with the load spreading at 1 in 4 from two-thirds of the pile length.	Double	Engine shell
Pipe Friction Loss Calculatorpipe-friction-calculator	Solve	V = (Q)/(A), h_f = f(L)/(D)(V^2)/(2g), Δ P = ρ g h_f Darcy (1857); Weisbach (1845); Colebrook-White (1939).	Double	Engine shell
Pipe Stress Analysispipe-stress-analysis	Direct	Δ = α L Δ T, S = (3 E D Δ)/(L^2), S_A = f(1.25 S_c + 0.25 S_h) ASME B31.3 §302.3.5 allowable stress range; guided-cantilever screening formula.	Double	Engine shell
Pipe Support Loadspipe-support-loads	Direct	— Pipe, insulation and contents over the span.	Double	Dedicated
Plasma (MHD) Field Calculatorplasma-magnetohydrodynamic-field-solver	Direct	V_A = (B_0)/(√(μ_0ρ)), c_s = (γ p)/(ρ), β = (2μ_0 p)/(B_0^(2)), c_(f,s)^(2) = (1)/(2) [(c_s^(2)+V_A^(2)) ± (c_s^(2)+V_A^(2))^(2)-4c_s^(2)V_A^(2)cos^(2)θ ] NRL Plasma Formulary (2023), Alfvén and magnetosonic speeds; standard ideal-MHD dispersion relation (e.g., Boyd & Sanderson, The Physics of Plasmas).	Double	Dedicated
Portal Frame Analysisportal-frame-analysis	Matrix	— Direct-stiffness linear static analysis under AISC 360 §C2, 12-degree-of-freedom 3D beam element.	Double	Dedicated
Power Factor Correction Calculatorpower-factor-correction-calculator	Direct	Q_c = P(tanφ_1 - tanφ_2), C = (Q_c)/(2π f V^2) IEEE 18 (shunt power capacitors); IEC 60831.	Double	Engine shell
Power Flow Calculatorpower-flow-calculator	Matrix	P_i = Σ_j V_i V_j (G_(ij)cosθ_(ij) + B_(ij)sinθ_(ij)) Grainger & Stevenson, Power System Analysis; the Newton-Raphson formulation follows the standard polar Jacobian.	Double	Engine shell
Pressure Vessel Shellpressure-vessel-shell	Direct	t = (P R)/(S E - 0.6P) ASME Boiler and Pressure Vessel Code, Section VIII Division 1, UG-27(c)(1).	Double	Engine shell
Prestressed Concrete Stressesprestressed-concrete-calculator	Direct	— Elastic fibre stresses with effective prestress.	Double	Dedicated
Process Capability Calculatorprocess-capability-calculator	Direct	C_p = (USL - LSL)/(6σ), C_(pk) = (min(USL - μ, μ - LSL))/(3σ) Standard capability indices; Cpk 1.33 minimum for existing processes, 1.67 for new ones.	Double	Engine shell
Projectile Motion Calculatorprojectile-motion-calculator	Direct	x = v_0cosθ t, y = h_0 + v_0sinθ t - (1)/(2)gt^2, t_f = (v_y + √(v_y^2 + 2gh_0))/(g), R = v_0cosθ t_f Standard vacuum ballistics; Newtonian kinematics.	Double	Engine shell
Protective Device Coordinationprotective-device-coordination	Direct	t = (TMS · 0.14)/((I/I_s)^(0.02) - 1), m = (t_(up))/(t_(down)) IEC 60255-151 standard inverse curve; margin convention from common protection practice.	Double	Engine shell
Psychrometric Calculatorpsychrometric-calculator	Solve	W = (0.621945 p_w)/(p-p_w); h = 1.006 T + W(2501 + 1.86 T); ln p_(ws) = (C_8)/(T)+C_9+C_(10)T+C_(11)T^2+C_(12)T^3+C_(13)ln T ASHRAE Handbook — Fundamentals 2017, Chapter 1: Equations 5 and 6 (Hyland–Wexler), 20, 32 and 33.	Double	Engine shell
Pump and System Curvepump-system-curve	Solve	H_(pump) = H_0 - aQ^2, H_(system) = H_(static) + kQ^2 Quadratic pump and system curves; affinity laws Q ∝ N, H ∝ N², P ∝ N³.	Double	Engine shell
Pump Power Calculatorpump-power-calculator	Direct	P_h = ρ g Q H, P_s = (P_h)/(η_p), P_m = (P_s)/(η_m), n_s = (n√(Q))/(H^(0.75)) Hydraulic Institute HI 14.6 / ISO 9906 pump performance standards.	Double	Engine shell
Quantum Monte Carlo Calculatorquantum-monte-carlo-many-body-solver	Simulateseeded	E_0 = (d)/(2) [ω + (N-1) ω^(2)+gN ], E_(VMC) = _T \| H \| _T _T \| _T = E_(loc)(R) _(\| _T\|^(2)) Harmonic-interaction (Moshinsky) model exact solution; variational Monte Carlo and the Metropolis algorithm — Metropolis et al., J. Chem. Phys. 21 (1953); Needs et al., J. Phys.: Condens. Matter 22 (2010).	Double	Dedicated
Quantum Tunneling Calculatorquantum-tunneling-probability-density-engine	Direct	T = [ 1 + (V_0^(2) sinh^(2)(κ L))/(4E(V_0-E)) ]^(-1), κ = (2m(V_0-E))/(ℏ^(2)), E < V_0 Griffiths, Introduction to Quantum Mechanics, finite rectangular barrier transmission (exact boundary-matching solution); WKB opaque-barrier limit T ≈ 16·E(V0−E)/V0²·e^(−2κL).	Double	Dedicated
Radiation Calculatorradiation-calculator	Direct	q = (σ (T_1^4 - T_2^4))/((1-ε_1)/(ε_1 A_1) + (1)/(A_1 F_(12)) + (1-ε_2)/(ε_2 A_2)) Stefan-Boltzmann law with the gray-diffuse two-surface enclosure; σ from CODATA 2018.	Double	Engine shell
Rankine Cycle Calculatorrankine-cycle-calculator	Direct	η = ((h_1 - h_2) - (h_4 - h_3))/(h_1 - h_4) Saturated steam properties from IAPWS-IF97; the cycle is the simple ideal Rankine with isentropic efficiencies applied to the endpoints.	Double	Engine shell
Rankine Regeneration Calculatorrankine-regeneration-calculator	Direct	y = (h_(fw) - h_f)/(h_2 - h_f) Energy balance on an open feedwater heater, with saturated properties from IAPWS-IF97.	Double	Engine shell
Rankine Reheat Calculatorrankine-reheat-calculator	Direct	η = ((h_1 - h_2) + (h_3 - h_4) - w_p)/((h_1 - h_6) + (h_3 - h_2)) Saturated properties from IAPWS-IF97 with a constant-cp superheat approximation.	Double	Engine shell
RC Time Constant Calculatorrc-time-constant-calculator	Direct	τ = RC, V_C(t) = V_(in)(1 - e^(-t/τ)), f_c = (1)/(2πτ), E = (1)/(2)CV^2 Standard first-order linear network solution; IEC 60617 for RC filter conventions.	Double	Engine shell
Rebar Development Calculatorrebar-development-calculator	Direct	l_d = (f_y ψ_t ψ_e ψ_s ψ_g)/(20 λ√(f'_c)) d_b ACI 318-19 Table 25.4.2.3 for the simplified equations and §25.5 for lap splices.	Double	Engine shell
Relativistic Orbital Precession Calculatorrelativistic-orbital-precession-matrix	Direct	Δ = (6π G M)/(c^(2) a (1-e^(2))) = (6πμ)/(c^(2)p), p = a(1-e^(2)) Einstein’s 1915 weak-field perihelion advance from the Schwarzschild geodesic (first post-Newtonian order). Einstein, “Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie” (1915); Weinberg, Gravitation and Cosmology; Misner, Thorne & Wheeler, Gravitation.	Double	Dedicated
Relief Valve Calculatorrelief-valve-calculator	Direct	A = (W)/(C K_d P_1) (TZ)/(M) API 520 Part I, Sizing, Selection and Installation of Pressure-Relieving Devices; orifice letters from API 526.	Double	Engine shell
Resistor Color Code Calculatorresistor-color-code-calculator	Convert	R = (10d_1 + d_2)· 10^(m) (4-band), R = (100d_1 + 10d_2 + d_3)· 10^(m) (5-band) IEC 60062, "Marking codes for resistors and capacitors".	Double	Engine shell
Response Surface Calculatorresponse-surface-calculator	Matrixseeded	y = b_0 + b_1x_1 + b_2x_2 + b_(12)x_1x_2 + b_(11)x_1^2 + b_(22)x_2^2; x_s = -(1)/(2)B^(-1)b Box & Wilson (1951), 'On the Experimental Attainment of Optimum Conditions'; Myers, Montgomery & Anderson-Cook, Response Surface Methodology.	Double	Engine shell
Retaining Wall Calculatorretaining-wall-calculator	Direct	K_a = (1-sinφ)/(1+sinφ); P_a = (1)/(2)K_aγ H^2; FS_(ot) = (Σ M_r)/(Σ M_o) Rankine earth pressure theory; stability factors and the bearing equation follow Das, Principles of Foundation Engineering, and the usual 1.5 working-stress targets.	Double	Engine shell
Reynolds Number Calculatorreynolds-number-calculator	Solve	Re = (ρ V D)/(μ), f = (64)/(Re) (laminar), (1)/(√(f)) = -2log_(10) ((ε)/(3.7D) + (2.51)/(Re√(f))) Reynolds (1883); Colebrook (1939); Moody (1944) chart.	Double	Engine shell
Room Load Calculatorhvac-room-load	Direct	Q = Σ U A Δ T + SHGC · A_g · G + Q_(int) + 1.2 · V · 1.005 · Δ T Steady-state cooling load; ASHRAE Fundamentals for the air properties.	Double	Engine shell
Sample Size Calculatorsample-size-calculator	Direct	n = ((z_(1-α/2) + z_(1-β))^2 σ^2)/(Δ^2) Standard power analysis for a two-sided test; normal approximation.	Double	Engine shell
Section Buildersection-builder	Direct	I_x = (b h^3 - (b - t_w) h_w^3)/(12), S_x = (I_x)/(h/2), r_x = (I_x)/(A) Parallel-axis theorem applied to the rectangles that make up the shape.	Double	Engine shell
Section Properties Calculatorsection-properties-calculator	Direct	I_(rect) = (bh^3)/(12), I_(circ) = (π d^4)/(64), S = (I)/(c), r = (I)/(A), σ = (M)/(S) Gere & Goodno, "Mechanics of Materials", appendix tables; EN 1993-1-1 for steel section properties.	Double	Engine shell
Seismic Base Shear Calculatorseismic-base-shear-calculator	Direct	C_s = min((S_(DS))/(R/I_e), (S_(D1))/(T (R/I_e))) ≥ C_(s,min), V = C_s W ASCE 7 equivalent lateral force procedure (§12.8); site coefficients from the hazard maps.	Double	Engine shell
Seismic Detailing Calculatorseismic-detailing-calculator	Direct	Σ M_(nc) ≥ 1.2 Σ M_(nb) ACI 318-19 Chapter 18: §18.6.2, §18.6.4, §18.7.3 and §18.8.4.	Double	Engine shell
Seismic Response Calculatorkinetic-seismic-structural-response-node	Matrix+ Time march	M u + C u + Ku = -Mr u_g(t), S_a = ω^2 S_d, S_v = ω S_d Linear MDOF base-excitation equation of motion with Newmark-β average-acceleration integration (β = 1/4, γ = 1/2) and pseudo-spectral ordinates; Chopra, Dynamics of Structures (base excitation, response spectrum); FEMA/NEHRP Recommended Seismic Provisions (modal response-spectrum analysis).	Double	Dedicated
Series & Parallel Resistance Calculatorseries-parallel-resistance-calculator	Direct	R_(series) = Σ R_i, (1)/(R_(parallel)) = Σ (1)/(R_i), P = I^2R Kirchhoff's circuit laws; standard passive-network analysis.	Double	Engine shell
Service Load Calculatorservice-load-calculator	Direct	L = 3,000 + 0.35 (L_(light) - 3,000) + … NFPA 70 Article 220 Part III: Table 220.12, Table 220.42, §220.53, Table 220.55, §220.54 and §220.60.	Double	Engine shell
Shear Wall Calculatorshear-wall-calculator	Direct	V_c = 0.17λ√(f'_c) h d + (N_u d)/(4 l_w), φ V_n = 0.75(V_c + V_s) ACI 318-19 §11.5.3; minimum horizontal steel §11.6.2.	Double	Engine shell
Short-Circuit Calculatorshort-circuit-calculator	Direct	I''_k = (c U_n)/(√(3) Z_k), i_p = κ √(2) I''_k IEC 60909-0 radial network; adiabatic check from IEC 60364-5-54.	Double	Engine shell
Slender Column Calculatorslender-column-calculator	Direct	δ = (C_m)/(1 - P_u/(0.75P_c)) ≥ 1, P_c = (π^2 EI)/((kl_u)^2) ACI 318-19 §6.6.4 (moment magnification), §6.6.4.4.4 (effective stiffness).	Double	Engine shell
Slope Stability Calculatorslope-stability-calculator	Direct	F = (Σ [(c'b + (W - ub)tanφ')/(m_α)])/(Σ W sinα) Bishop (1955), simplified method; the ru pore-pressure simplification is standard practice.	Double	Engine shell
Snow Drift Calculatorsnow-drift-calculator	Direct	h_d = 0.43 l_u^(1/3)(p_g + 10)^(1/4) - 1.5 ASCE 7-22 §7.7.1, evaluated in feet and psf and converted.	Double	Engine shell
Snow Load Calculatorsnow-load-calculator	Direct	p_f = 0.7 C_e C_t I_s p_g; p_s = C_s p_f; h_d = 0.43 l_u^(1/3)(p_g+10)^(1/4)-1.5 ASCE/SEI 7-22, Chapter 7: Equations 7.3-1 and 7.4-1, Tables 7.3-1, 7.3-2 and 1.5-1, Figure 7.4-1, §7.3.4 minimum and §7.7.1 drift.	Double	Engine shell
Solar Panel Calculatorsolar-panel-calculator	Direct	P_(array) = (E_(daily))/(PSH (1-η_(loss))), N = (P_(array)· 1000)/(P_(panel)), C_(batt) = (E_(daily)· autonomy)/(DoD) IEC 62548 (PV array design); NREL PVWatts derate conventions.	Double	Engine shell
Soot and Ash Radiation Calculatorparticulate-radiation-calculator	Direct	ε = 1 - e^-(k_(gas) + k_(soot) + k_(ash))L Soot k = 3.6 f_v/λ (Beér); ash k = 1.5 c/(ρ d); gas from the WSGG model.	Double	Engine shell
Space Truss Calculatorspace-truss-calculator	Matrix	K u = F, N = (EA)/(L)(Δ u c_x + Δ v c_y + Δ w c_z) Direct stiffness method, three degrees of freedom per node, pin-jointed members.	Double	Engine shell
Spring Rate Calculatorspring-rate-calculator	Direct	k = (G d^4)/(8 D^3 N), C = (D)/(d), K_w = (4C-1)/(4C-4) + (0.615)/(C), τ = K_w(8FD)/(π d^3) Wahl (1963) coil spring correction; Shigley's Mechanical Engineering Design ch. 10; ASTM A228 / A231 material shear moduli.	Double	Engine shell
Steam Pipe Calculatorsteam-pipe-calculator	Direct	A = ( m v_g)/(V); d = (4A)/(π) IAPWS-IF97 saturated steam properties; velocity sizing practice from Spirax Sarco and Crane TP-410.	Double	Engine shell
Steam Trap Calculatorsteam-trap-calculator	Direct	m = 0.65 A√(2ρΔ P); x = (h_(f1) - h_(f2))/(h_(fg2)) Liquid orifice discharge for trap capacity; flash from the saturated steam table (IAPWS-IF97).	Double	Engine shell
Steel Connection Designsteel-connection-design	Direct	R_n = F_(nv) A_b n, R_(brg) = 2.4 d t F_u, R_(block) = min(0.6F_uA_(nv) + F_uA_(nt), 0.6F_yA_(gv) + F_uA_(nt)) AISC 360-22 §J3.2, §J3.6, §J3.10, §J4.3; φ = 0.75.	Double	Engine shell
Steel Fire Resistance Checkfire-resistance-check	Time march	θ_(cr) = 39.19ln ((1)/(0.9674 μ_0^(3.833)) - 1) + 482 EN 1993-1-2 §4.2.4 (critical temperature) and §4.2.5.2 (unprotected heating).	Double	Dedicated
Steel Member Code Checksteel-member-code-check	Direct	M_p = F_y Z_x, L_p = 1.76 r_y√(E/F_y), φ M_n = 0.9 M_n, utilisation = (demand)/(capacity) AISC 360-22, chapters F (flexure), G (shear), E (compression) and L (serviceability); EN 1993-1-1, 6.2 and 6.3.	Double	Engine shell
Steel Section Databasesteel-section-database	Direct	— AISC Shapes Database v15.0, converted to SI; curated doubly-symmetric W-shapes.	Double	Dedicated
Storage Tank Shellstorage-tank-design	Direct	— API 650 §5.6 one-foot method for shell thickness.	Double	Dedicated
Stormwater Runoff Calculatorstormwater-runoff-calculator	Direct	Q = C i A; Q_(depth) = ((P - 0.2S)^2)/(P + 0.8S) Rational method (ASCE / FHWA HEC-22); NRCS curve number from TR-55; time of concentration from Kirpich.	Double	Engine shell
Structural Dynamics Calculatormulti-degree-of-freedom-structural-dynamics-solver	Matrix	M u + C u + Ku = -Mr a_g(t), (K - ω_i^2 M) φ_i = 0 Modal analysis and Newmark-β direct integration of MDOF systems; Chopra, Dynamics of Structures; Bathe, Finite Element Procedures (Newmark average-acceleration method, β = 1/4, γ = 1/2); shear-building closed-form frequencies ω_i = 2√(k/m)·sin((2i−1)π/(2(2n+1))).	Double	Dedicated
Structural Reliability Calculatorstructural-reliability-calculator	Simulateseeded	β = (μ_R - μ_D - μ_L)/(√(σ_R^2 + σ_D^2 + σ_L^2)); P_f = (-β) Hasofer & Lind (1974); Ditlevsen & Madsen, Structural Reliability Methods; EN 1990 for the β = 3.5 calibration.	Double	Engine shell
Thermal Bridge Calculatorthermal-bridge-calculator	Direct	— H = ψ·L·ΔT; ψ from the detail, ISO 10211 or the manufacturer.	Double	Dedicated
Thermal Expansion Calculatorthermal-expansion-calculator	Direct	Δ L = α L Δ T, ε = α Δ T, σ = E α Δ T, F = σ A Standard isotropic thermoelasticity; α and E values from ASM Handbook and MatWeb material tables.	Double	Engine shell
Three-Phase Power Calculatorthree-phase-power-calculator	Direct	S = √(3) V_L I_L, P = Scosφ, Q = Ssinφ, V_(ph) = (V_L)/(√(3)) (star), I_(ph) = (I_L)/(√(3)) (delta) IEC 60038 (standard voltages); balanced-load power relations per IEEE 141.	Double	Engine shell
Timber Beam Calculatortimber-beam-calculator	Direct	f_b = (M)/(S) ≤ F_b'; F_b' = F_b C_D C_F C_V C_L C_r; Δ = (5wL^4)/(384EI) NDS for Wood Construction (AWC), §3.3 and Tables 2.3.2, 4A and 4.3.1; reference values from the NDS Supplement.	Double	Engine shell
Tolerance Stack-Up Calculatortolerance-stackup-calculator	Direct	T_(wc) = Σ t_i, T_(rss) = √(Σ t_i^2) Worst-case (arithmetic) and statistical (root-sum-square) tolerance analysis, standard practice in mechanical design.	Double	Engine shell
Torsional Vibrationtorsional-vibration	Direct	— Free–free torsional mode of a uniform shaft.	Double	Dedicated
Transformer Sizing Calculatortransformer-sizing-calculator	Direct	S = (P)/(cosφ); I = (S)/(√(3) V); I_(sc) = (I_(FL))/(Z%/100) ANSI C57 and IEEE C57.12 for ratings and impedance; the ASA regulation approximation from IEEE Std 141 (Red Book).	Double	Engine shell
Transient Heat Calculatortransient-heat-calculator	Time march	θ = e^(-t/τ) or θ_0 = C_1 e^(-ζ_1^2 Fo) Lumped capacitance and the one-term approximation of the exact series; coefficients from Incropera & DeWitt Table 4.1.	Double	Engine shell
Truss Analysis Calculatortruss-analysis-calculator	Matrix	K·u = F, N = (EA)/(L)(Δ ucosθ + Δ vsinθ) Direct stiffness method for a two-dimensional pin-jointed truss.	Double	Engine shell
Turbulent Boundary Layer Calculatorturbulent-boundary-layer-spectral-closure-engine	Direct	Re_τ = (u_τδ)/(ν), y^+ = (y u_τ)/(ν), E_(11)(k_1) = (k_1 E_(11)^(HIT))/(u_τ^2)((y)/(δ))^(n) Pope (2000), "Turbulent Flows"; the closure coefficients follow a 2025 JFM spectral formulation.	Double	Dedicated
Two-Phase Flow Calculatortwo-phase-flow-calculator	Direct	Δ P = φ_l^2 Δ P_l, X = ((1-x)/(x))^(0.9)((ρ_g)/(ρ_l))^(0.5)((μ_l)/(μ_g))^(0.1) Lockhart-Martinelli separated flow; Zivi void correlation.	Double	Engine shell
Two-Phase Relief Calculatortwo-phase-relief-calculator	Direct	G = 0.66 (P_1)/(v_0 ω), ω = 9.1 API 520 Part I Appendix C, the omega method for flashing service.	Double	Engine shell
Two-Way ANOVA Calculatortwo-way-anova-calculator	Direct	y_(ijk) = μ + α_i + β_j + (αβ)_(ij) + ε_(ijk) Two-way analysis of variance with interaction, balanced design.	Double	Engine shell
Two-Way Slab Calculatortwo-way-slab-calculator	Direct	M_0 = (w_u l_2 l_n^2)/(8), v_u = (V_u)/(b_o d) ≤ φ v_c ACI 318-19 §8.10 (direct design method) and §22.6.5.2 (punching).	Double	Engine shell
Unit Converterunit-converter	Convert	y = (x · f_(from) + o_(from) - o_(to))/(f_(to)) SI Brochure (BIPM) for metric definitions; NIST Handbook 44 and international yard-and-pound agreement for US customary definitions (1 in = 25.4 mm, 1 lb = 0.45359237 kg); ISO 80000 for BTU and thermochemical calorie.	Double	Dedicated
Vibration Calculatoroscillatory-kinetic-vibration-engine	Direct	X = (F_0)/(√((k - mω^2)^2 + (cω)^2)), φ = atan2(cω, k - mω^2), M = (1)/(√((1-r^2)^2 + (2ζ r)^2)), r = (ω)/(ω_n) Steady-state response of a damped SDOF oscillator to harmonic forcing; Rao, Mechanical Vibrations; MIT OCW 2.003/18.03 forced-vibration notes.	Double	Dedicated
Voltage Divider Calculatorvoltage-divider-calculator	Direct	V_(out) = V_(in)(R_2)/(R_1+R_2), V_(loaded) = V_(in)(R_2 R_L)/(R_1 + R_2 R_L), R_(th) = R_1 R_2 Thévenin equivalent of a resistive network; IEC 60038 for nominal low-voltage levels.	Double	Engine shell
Voltage Drop Calculatorvoltage-drop-calculator	Direct	V_d = 2IRL (single phase), V_d = √(3)IRL (three phase), % = (V_d)/(V)× 100 NEC Chapter 9 Table 8 (conductor DC resistance); NEC 210.19(A) informational note on 3% / 5% voltage drop.	Double	Dedicated
Waveguide Attenuation Calculatorelectromagnetic-waveguide-attenuation-core	Directseeded	f_(c,10) = (c)/(2a√(ε_r)), β = k_0^(2)-k_c^(2), R_s = (ωμ_0)/(2σ), α_c = (R_s (2b k_c^(2)+a k_0^(2)))/(a b β k_0 η_0), α_(dB/m) = 8.686 α_c Pozar, Microwave Engineering, 4th ed., TE10 attenuation of a rectangular waveguide (Ch. 3); conductor loss cross-checked against NIST Technical Note 2109; surface resistance R_s = √(ωμ0/2σ).	Double	Dedicated
Weibull Reliability Calculatorweibull-reliability-calculator	Direct	R(t) = e^(-(t/η)^β), h(t) = (β)/(η)((t)/(η))^(β-1), MTBF = η (1+(1)/(β)) Abernethy, "The New Weibull Handbook", 5th ed.	Double	Engine shell
Wire Gauge Calculatorwire-gauge-calculator	Direct	d = 0.127 · 92^((36-n)/39) mm, A = (π d^2)/(4), R = (ρ L)/(A), V_d = 2IRL ASTM B258 (AWG diameters); NEC Article 310.16 (ampacity tables); IEC 60228 for metric equivalents.	Double	Engine shell
401(k) Calculator401k-calculator	Schedule	e_t = min(s_t · c, limit), m_t = μ · min(e_t, s_t · κ), B_(t+1) = (B_t + e_t + m_t)(1+r) IRC §402(g) elective-deferral limit; typical safe-harbour match design (50% of the first 6%).	Double	Engine shell
529 College Savings Calculator529-college-savings-calculator	Schedule	B_n = B_0(1+r)^n + c ((1+r)^n-1)/(r); penalty = E_(nq) (t + 0.10) IRC §529 for qualified tuition programmes; the 10% additional tax is in §529(c)(6). State deductions follow each state's own statute.	Double	Engine shell
Alternative Minimum Tax Calculatoramt-calculator	Direct	AMT = max(0, T_(min) - T_(reg)) IRS Rev. Proc. 2025-32 §3.10 (2026 exemption, phase-out and 28% threshold).	Double	Dedicated
American Option Calculatorlongstaff-schwartz-american-option-engine	Simulate	V_0 = E[ e^(-rτ) h_τ(S_τ) ], C_t(S_t) ≈ Σ_(j=0)^(3) β_j L_j((S_t)/(K)), exercise at t if h_t(S_t) > C_t(S_t) Longstaff & Schwartz (2001), "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies 14(1); Cox, Ross & Rubinstein (1979) binomial benchmark; Hull, Options, Futures, and Other Derivatives.	Double	Dedicated
Amortization Calculatoramortization-calculator	Schedule	M = P (r(1+r)^(n))/((1+r)^(n)-1), r = (APR)/(1200), n = months Standard annuity-immediate amortization formula (Broverman, Mathematics of Investment and Credit), evaluated with expm1/log1p for numerical stability. The APR is treated as a nominal annual rate compounded monthly — the usual US consumer-loan payment convention. Reg Z Appendix J defines the actuarial APR itself, which includes finance charges and is not simply the note rate divided by twelve.	Decimal.js	Dedicated
Annuity Calculatorannuity-calculator	Direct	PV = PMT·(1-(1+i)^(-n))/(i); FV = PMT·((1+i)^(n)-1)/(i) Broverman, Mathematics of Investment and Credit, ch. 2; the same identity underlies the Reg Z amortisation convention.	Double	Engine shell
APR Calculatorapr-calculator	Solve	P - F = M · (1 - (1+a)^(-n))/(a), M = (P i)/(1-(1+i)^(-n)) Regulation Z, 12 CFR §1026.22 (APR); standard amortising payment formula.	Double	Engine shell
APY Calculatorapy-calculator	Direct	APY = (1 + (r)/(n))^(n) - 1, APY_(∞) = e^(r) - 1, i = (r)/(n) Truth in Savings Act (Regulation DD) definition of annual percentage yield; standard effective-rate algebra.	Double	Engine shell
ARM Calculatorarm-calculator	Schedule	r_(reset) = min(i + m, r_0 + cap_(periodic), r_0 + cap_(life)) Regulation Z (12 CFR §1026.20) adjustable-rate reset: index plus margin, periodic and lifetime caps.	Double	Engine shell
Asset Location Calculatorasset-location-calculator	Direct	— After-tax future value in a taxable versus a tax-deferred account, applying the IRC §1 and §408 treatment of contributions and growth.	Double	Dedicated
Auto Lease Calculatorauto-lease-calculator	Direct	M = (C - R)/(n) + (C + R)· MF; APR = 2400· MF Standard lease algebra as used by the Federal Reserve's leasing disclosure (Reg M) and by ALG residual guides.	Double	Engine shell
Auto Loan Calculatorauto-loan-calculator	Schedule	F = Price - Down - Trade + Tax + Fees, PMT = (F · i)/(1-(1+i)^(-n)), i = (APR)/(12) Standard vehicle-retail financing under Regulation Z (12 CFR §1026) APR disclosure; state motor-vehicle sales-tax treatment of trade-ins.	Double	Engine shell
Autocallable Note Calculatorautocallable-note-calculator	Simulateseeded	S_(t+Δ) = S_texp[(r-q- 12σ^2)Δ + σ√(Δ) Z] Standard Monte Carlo structured-product practice; the payoff convention follows the Phoenix autocallable described in Bouzoubaa & Osseiran, Exotic Options and Hybrids.	Double	Engine shell
Average Return Calculatoraverage-return-calculator	Direct	— CAGR is the geometric mean and the arithmetic average is linear (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
Black-Litterman Portfolio Calculatorblack-litterman-portfolio-equilibrium-engine	Matrix	= δ Σ w_(mkt), E[R] = [(τΣ)^(-1) + P^( )Ω^(-1)P]^(-1)[(τΣ)^(-1) + P^( )Ω^(-1)Q], w^(*) = (δΣ)^(-1)E[R] Black & Litterman (1992), "Global Portfolio Optimization," Financial Analysts Journal; He & Litterman (1999) on calibrating the view-uncertainty matrix; Idzorek (2007) on confidence-based Omega.	Double	Engine bridge
Black-Scholes Options Calculatorblack-scholes-options-pricing-core	Direct+ Solve	C = S e^(-qT) N(d_1) - K e^(-rT) N(d_2), d_1 = (ln(S/K) + (r - q + (1)/(2)σ^2)T)/(σ√(T)), d_2 = d_1 - σ√(T) Black & Scholes (1973), "The Pricing of Options and Corporate Liabilities"; Merton (1973) extension to continuous dividend yields; Hull, Options, Futures, and Other Derivatives (closed-form Greeks and put-call parity).	Double	Engine bridge
Boat Loan Calculatorboat-loan-calculator	Schedule	— Level payment amortisation at a fixed rate (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
Bond Duration Calculatorbond-duration-calculator	Direct	P = Σ_(t=1)^(n)(c)/((1+y/f)^t) + (F)/((1+y/f)^n), D = (Σ (t/f)PV_t)/(P), D^(*) = (D)/(1+y/f) Fabozzi, "Bond Markets, Analysis and Strategies", ch. 4–5.	Double	Engine shell
Bond Yield Calculatorfixed-income-bond-yield-matrix	Solve+ Direct	P(y) = Σ_(k=1)^(N) (CF_k)/((1 + y/m)^k), D_(Mac) = (1)/(P)Σ_(k=1)^(N) t_k PV_k, D_(mod) = (D_(Mac))/(1 + y/m) Frank J. Fabozzi, Bond Markets, Analysis, and Strategies — present-value pricing of bonds and the measurement of duration and convexity.	Double	Dedicated
Break-Even Calculatorbreak-even-calculator	Direct	CM = P - V, Q^() = (F)/(P-V), MoS = (Q - Q^())/(Q), π = Q(P-V) - F Horngren, Datar & Rajan, "Cost Accounting", ch. 3 (cost-volume-profit analysis).	Double	Engine shell
Budget Calculatorbudget-calculator	Direct	needs≤ 50%, wants≤ 30%, savings≥ 20%, Σ shares=100% Warren & Tyagi, All Your Worth (2005) — the 50/30/20 heuristic, not a regulatory standard.	Double	Engine shell
Burn Rate and Runwayburn-rate-runway	Time march	cash_m = cash_(m-1) + R_m - E_m Monthly cash roll-forward with compounding revenue and expenses (Brigham & Ehrhardt, Financial Management, cash budgeting).	Double	Engine shell
Business Loan Calculatorbusiness-loan-calculator	Schedule	— Level amortisation plus the DSCR coverage test; SBA SOP 50 10 sets the 1.25× minimum.	Double	Dedicated
CAGR Calculatorcagr-calculator	Direct	CAGR = ((V_n)/(V_0))^(1/n) - 1, g_(real) = (1+CAGR)/(1+π) - 1, t_2 = (ln 2)/(ln(1+CAGR)) Damodaran, "Investment Valuation", ch. 4; Fisher (1930) on real versus nominal rates.	Double	Engine shell
Canadian Mortgage Calculatorcanadian-mortgage-calculator	Direct	— Interest Act (R.S.C. 1985, c. I-15) s. 6: nominal rate compounded semi-annually, paid monthly.	Double	Dedicated
Cap Rate Calculatorcap-rate-calculator	Direct	cap = (NOI)/(P), DSCR = (NOI)/(DS), CoC = (NOI - DS)/(E) Appraisal Institute, "The Appraisal of Real Estate", 15th ed.	Double	Engine shell
Cap Table Calculatorcap-table-calculator	Solve	p = (pre-money)/(S_(existing) + P), P = (q)/(1-q)(S_(existing) + n) Standard priced-round arithmetic with a pre-money pool, following the NVCA model legal documents.	Double	Engine shell
Capital Allocation Calculatorcapital-allocation-matrix	Matrix	w_T ∝ Σ^(-1)(μ - r_f 1), E[R_c] = r_f + y (E[R_T] - r_f), y^(*) = (E[R_T] - r_f)/(A σ_T^(2)) Markowitz (1952) mean-variance portfolio selection; Tobin (1958) separation theorem; two-asset tangency weights from the inverse covariance matrix; quadratic (mean-variance) utility.	Double	Dedicated
Capital Gains Tax Calculatorcapital-gains-tax-calculator	Direct	T = Σ_i τ_i · G_i + 0.038 · min(NII, MAGI - threshold) IRC §1(h) (2025 long-term rates, Rev. Proc. 2024-40); IRC §1411 (net investment income tax).	Double	Engine shell
Caplet Bootstrap Calculatorcaplet-bootstrap-calculator	Schedule	Cap_n = Σ_(i=1)^(n) Caplet_i; Caplet_n = Cap_n - Cap_(n-1) Brace, Gatarek & Musiela (1997) for the LIBOR market model; the caplet identity is standard Black (1976) cap pricing.	Double	Engine shell
CAPM Calculatorcapm-asset-equilibrium-core	Direct	E[R_i] = R_f + β_i(E[R_m] - R_f), β_i = (Cov(R_i, R_m))/(Var(R_m)) = (ρ_(iM) σ_i)/(σ_m) Sharpe (1964), "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk"; Lintner (1965); Mossin (1966); textbook treatment in Hull, Options, Futures, and Other Derivatives.	Double	Dedicated
Cash Back vs Low Interestcash-back-vs-low-interest-calculator	Direct	— Both offers compared over the same term and price as present values (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
CD Calculatorcd-calculator	Direct	APY = (1 + (r)/(n))^n - 1, M = P(1 + (r)/(n))^(nt) Truth in Savings Act, 12 CFR §1030.4 (APY definition); standard compound-interest formula.	Double	Engine shell
CDO Tranche Calculatorcdo-tranche-calculator	Direct	p(M) = [( ^(-1)(PD) - √(ρ) M)/(√(1-ρ))]; L = LGD· p(M) Vasicek (1987) loan portfolio value; Li (2000) for the Gaussian copula applied to CDOs; BCBS (2005) for the regulatory use.	Double	Engine shell
Charitable Trust Calculatorcharitable-trust-calculator	Direct	CRUT: V(1-p)^n; CRAT: V(1-p a(n,r)); CLAT: V - A a(n,r) IRC §664 (charitable remainder trusts), §7520 (valuation of annuities and split interests), §170(f)(2) (charitable lead trusts).	Double	Engine shell
CIR Interest Rate Calculatorcox-ingersoll-ross-stochastic-term-engine	Direct	dr_t = κ(θ - r_t) dt + σ√(r_t) dW_t, P(t,T) = A(t,T) e^(-B(t,T)r_t), γ = √(κ^2 + 2σ^2) Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985), "A Theory of the Term Structure of Interest Rates," Econometrica 53(2), 385-407 (closed-form affine bond price).	Double	Dedicated
Closing Costs Calculatorclosing-costs-calculator	Direct	points = L× p; prepaid = (L r d)/(365); cash to close = D + Σ C The Loan Estimate and Closing Disclosure forms required by the TILA-RESPA integrated disclosure rule (12 CFR §1026.19) define the line items.	Double	Engine shell
College Cost Calculatorcollege-cost-calculator	Time march	— Cost inflation compounding to the first year of study, on NCES/IPEDS tuition data.	Double	Dedicated
Commission Calculatorcommission-calculator	Direct	— Marginal tiering: each rate applies only to the slice above its threshold (Horngren et al., Cost Accounting).	Double	Dedicated
Commodity Mean-Reversion Calculatorcommodity-mean-reversion-schwartz-engine	Direct	dX_t = κ(a - X_t) dt + σ dZ_t, X_t=ln S_t, F(S,T) = exp (e^(-κ T)ln S + (1-e^(-κ T))a^(*) + (σ^2)/(4κ)(1-e^(-2κ T)) ) Schwartz, E. S. (1997), "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance 52(3), 923-973 (Model 1).	Double	Dedicated
Compound Interest Calculatorcompound-interest-calculator	Direct	A = P(1 + (r)/(n))^(nt), APY = (1 + (r)/(n))^(n) - 1 Standard compound-interest future value and effective annual yield (Broverman, Mathematics of Investment and Credit; any algebra-of-finance text). Continuous mode uses A = Pe^{rt}, evaluated in daily steps. Contributions are added monthly before that month's compounding.	Decimal.js	Dedicated
Construction Loan Calculatorconstruction-loan-calculator	Schedule	I = L · r · (m)/(12) · d, d = 0.5 Interest capitalised on the average outstanding balance, the standard construction draw convention (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Corporate Debt Calculatorcorporate-debt-financing-node	Direct	P = Σ_(t=1)^(n)(C)/((1+y)^(t)) + (F)/((1+y)^(n)), V_L = V_U + tD, WACC = (E)/(V)k_e + (D)/(V)k_d(1-t) Modigliani & Miller (1963), corporate taxes and the value of the firm; Sharpe (1964) CAPM; standard bond-pricing and APV conventions (Brealey, Myers & Allen, Principles of Corporate Finance).	Double	Dedicated
Covenant Headroomcovenant-headroom	Direct	leverage = (net debt)/(EBITDA), cover = (EBITDA)/(interest) Lender definitions: leverage as a maximum, cover and DSCR as minimums (Brigham & Ehrhardt, Financial Management, ratio analysis).	Double	Engine shell
Credit Card Payoff Calculatorcredit-card-payoff-calculator	Schedule	r = (APR)/(1200), B_(k+1) = B_k (1+r) - pay_k, surplus paid to the priority debt Revolving-credit amortisation with monthly interest = balance × APR ÷ 12, minimums paid first, simulated month by month (Broverman, Mathematics of Investment and Credit).	Decimal.js	Dedicated
Credit Default Swap (CDS) Calculatorcredit-default-swap-hazard-rate-solver	Solve+ Direct	S(t) = exp (-∫_0^t λ(u) du), s Σ_i α_i D(t_i) S(t_i) = (1-R)Σ_i D(t_i) [S(t_(i-1)) - S(t_i) ] O'Kane, D. & Turnbull, S. (2003), "Valuation of Credit Default Swaps," Lehman Brothers Fixed Income Quantitative Research; ISDA Standard CDS Model (reduced-form hazard-rate pricing).	Double	Dedicated
Credit Risk Capital Calculatorcredit-risk-capital-calculator	Direct	CVA ≈ LGD · EPE · PD(t) · DF, RWA = E · RW Basel standardised approach; flat-exposure CVA approximation.	Double	Engine shell
Currency Convertercurrency-converter	Convert	A_(to) = A_(from) × (X_(to))/(X_(from)) × (1 - f) European Central Bank euro foreign exchange reference rates (daily fixing, 16:00 CET).	Double	Dedicated
CVA Hedge and Capital Calculatorcva-capital-calculator	Directseeded	CVA ≈ LGD ·(1-e^(-λ T))· DF; K = [LGD N(·) - PD LGD] MA Basel II/III IRB corporate formula (BCBS 128, ¶272); CVA as the risk-neutral expected loss on expected positive exposure.	Double	Engine shell
DCF Valuation Calculatordiscounted-cash-flow-valuation-core	Direct	FCFF = EBIT (1-T) + D&A - CapEx - Δ NWC, EV = Σ_(t=1)^(n) (FCFF_t)/((1+WACC)^t) + (TV)/((1+WACC)^n), TV = (FCFF_(n+1))/(WACC - g) Standard corporate-finance treatment as in Brealey, Myers, and Allen, Principles of Corporate Finance (valuing a business by discounted cash flow); Gordon-growth terminal value after Gordon and Shapiro (1956).	Double	Dedicated
Debt Consolidation Calculatordebt-consolidation-calculator	Schedule	APR_w = (Σ b_i r_i)/(Σ b_i); I_(saved) = I_(current) - I_(loan) Level-payment amortisation with the weighted average taken by balance, the convention lenders quote (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Debt Sculptingdebt-sculpting	Schedule	— Debt capacity as the present value of the maximum annual service (Brealey, Myers & Allen, Principles of Corporate Finance).	Double	Dedicated
Debt Snowball Calculatordebt-snowball-calculator	Schedule	B_i arrow B_i(1 + (r_i)/(12)) - min_i, pool = extra + Σ_(cleared) min_i, snowball: argmin B_i, avalanche: argmax r_i Consumer debt-rollover simulation with minimum-payment conventions for revolving credit (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Debt-to-Income Calculatordebt-to-income-calculator	Direct	DTI_(back) = (housing + other debt)/(gross monthly income) Consumer Financial Protection Bureau qualified-mortgage standards (43% back-end); Fannie Mae and FHA underwriting guidelines.	Double	Engine shell
Depreciation Calculatordepreciation-calculator	Schedule	SL: D = (C-S)/(n), DDB: D_t = BV_(t-1)·(2)/(n), SYD: D_t = (C-S)(n-t+1)/(n(n+1)/2) IAS 16 (property, plant and equipment) and ASC 360 for financial-reporting depreciation; standard accounting texts for the SL, DDB-with-switch and SYD schedules. These are book methods — IRS Publication 946 MACRS tables use different conventions (half-year, no salvage) and are not implemented here.	Double	Engine shell
Development Feasibilitydevelopment-feasibility	Direct	— Residual land value after build cost, fees and profit (Appraisal Institute, The Appraisal of Real Estate).	Double	Dedicated
Discount Calculatordiscount-calculator	Direct	P_1 = P(1-d_1), P_2 = P_1(1-d_2), effective = 1-(1-d_1)(1-d_2) Standard retail markdown arithmetic (Horngren et al., Cost Accounting).	Double	Engine shell
Distribution Waterfalldistribution-waterfall	Schedule	catch-up = pref × (c)/(1 - c) European (whole-fund) waterfall with a simple non-compounding preference, following the ILPA waterfall and reporting standards.	Double	Engine shell
Dividend Reinvestment Calculatordividend-reinvestment-calculator	Schedule	n_(t+1) = n_t(1 + (d_0(1+g)^t)/(P_t)); yield on cost = (D_t)/(cost) Standard dividend-reinvestment arithmetic; the yield-on-cost convention follows the CFA Institute's equity income treatment.	Double	Engine shell
Down Payment Calculatordown-payment-calculator	Schedule	S_n = S_0(1+i)^n + c ((1+i)^n - 1)/(i) Homeowners Protection Act, 12 USC §4902, for the 78% automatic termination and 80% request thresholds.	Double	Engine shell
DSCR Calculatordscr-calculator	Direct	DSCR = (NOI)/(annual debt service) Commercial underwriting covenant, typically 1.20×–1.35×; SBA SOP 50 10 requires 1.25× for 7(a) loans.	Double	Engine shell
Dual-Curve Swap Calculatordual-curve-swap-calculator	Directseeded	NPV = NΣ_i τ_i (f_i - K) DF_i^(OIS) Post-crisis swap pricing convention (OIS discounting); see Hull & White, 'The Valuation of Collateralized Derivatives'.	Double	Engine shell
Dynasty Trust Calculatordynasty-trust-calculator	Schedule	inclusion = 1 - (X_(allocated))/(V); GST = 0.40 × V × inclusion IRC §2601–2664 (generation-skipping transfer tax), §2632 (allocation of exemption); state estate and trust taxation.	Double	Engine shell
Emergency Fund Calculatoremergency-fund-calculator	Schedule	target = S × m, B_n = B_(n-1)(1 + (apy)/(12)) + c Standard sinking-fund recursion with monthly compounding; target follows the conventional months-of-essential-spend rule used by CFPB and FDIC consumer guidance.	Double	Engine shell
Estate Tax Calculatorestate-tax-calculator	Direct	T = 0.40 × max(0, E - D - X) IRC §2001 (estate tax), §2010(c) (basic exclusion, portability), §2503(b) (annual gift exclusion).	Double	Engine shell
Expected Loss Calculatorexpected-loss-calculator	Direct	EL = PD × LGD × EAD Basel/IFRS 9/CECL expected-loss framework.	Double	Engine shell
Expected Shortfall Calculatorexpected-shortfall-calculator	Solve	ES_α = μ + σ(φ(z_α))/(1-α) Basel Committee, Minimum capital requirements for market risk (d457, 2019), §3 for the 97.5% ES; McNeil, Frey & Embrechts, Quantitative Risk Management, ch. 2 for the closed forms.	Double	Engine shell
Federal Income Tax Calculatorfederal-income-tax-calculator	Direct	T = Σ_i τ_i · (min(I, U_i) - L_i), I = max(0, G - D_(pre) - D_(std)) IRS Rev. Proc. 2024-40 (2025 brackets and standard deduction), 26 U.S.C. §1.	Double	Engine shell
FHA Loan Calculatorfha-loan-calculator	Schedule	MIP_(annual) = rate(LTV, loan) × (B + 0.0175B) HUD Handbook 4000.1 II.A.4.d for the premium schedule; the 2025 FHA floor is $524,225 for a one-unit property.	Double	Engine shell
Forex & Currency Calculatorcross-border-forex-liquidity-node	Direct	F = S e^((r_d - r_f - b)T), b = r_d - r_f - (1)/(T)ln (F)/(S), r_f^(hedged) = r_f + (1)/(T)ln (F)/(S) Covered interest rate parity (continuous-compounding form); Du, Tepper & Verdelhan (2018), "Deviations from Covered Interest Rate Parity," Journal of Finance 73(3), 915-957; BIS Quarterly Review on the cross-currency basis.	Double	Dedicated
FRTB GIRR Calculatorfrtb-sa-calculator	Direct	WS_k = RW_k s_k; ρ_(kl) = max(e^(-θ\|T_k-T_l\|/min(T_k,T_l)), 0.40); K = Σ WS_k^2 + Σ_(k≠ l)ρ_(kl) WS_k WS_l BCBS MAR21 (FRTB standardised approach), general interest rate risk delta charge, intra-bucket aggregation.	Double	Engine shell
Fund Metrics Calculatorfund-metrics-tvpi-dpi	Solve	TVPI = (D + NAV)/(P), DPI = (D)/(P), Σ (CF_t)/((1+r)^t) = 0 TVPI, DPI and IRR by bisection on the dated flows, per the ILPA reporting template.	Double	Engine shell
Future Value Calculatorfuture-value-calculator	Time march	— Compound growth with monthly contributions at the monthly-equivalent rate (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
GARCH Volatility Calculatorgarch-volatility-forecasting-solver	Schedule	σ_t^2 = ω + α ε_(t-1)^2 + β σ_(t-1)^2, E_t[σ_(t+h)^2] = σ^2 + (α + β)^(h-1)(σ_(t+1)^2 - σ^2), σ^2 = (ω)/(1-α-β) Engle (1982) for ARCH; Bollerslev (1986), "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics 31, for GARCH; forecast algebra as in standard time-series texts (e.g. Tsay, Analysis of Financial Time Series).	Double	Dedicated
GDP & Macroeconomics Calculatormacroeconomic-gdp-output-engine	Direct	GDP = C + I + G + X - M, Real GDP = (Nominal GDP)/(Deflator/100), g_(ann) = (1+g_(QoQ))^(4) - 1 US Bureau of Economic Analysis (BEA) expenditure approach and implicit GDP price deflator; World Bank production (value-added) approach; standard annualization of quarterly growth.	Double	Dedicated
Gift Tax Calculatorgift-tax-calculator	Direct	G_(taxable) = G - D_(marital) - D_(charity) - 19,000 × n IRC §2503(b) annual exclusion and §2010(c) basic exclusion, at the 2025 amounts from Rev. Proc. 2024-40; rate schedule at §2001(c).	Double	Engine shell
GRAT and IDGT Sale Calculatorgrat-idgt-calculator	Schedule	GRAT gift = V - A a(n,r); remainder = V(1+g)^n - A((1+g)^n-1)/(g) IRC §2702 (retained interests), §7520 (valuation); the AFR is published monthly under §1274.	Double	Engine shell
GST and Charitable Estate Calculatorgst-charitable-estate-calculator	Direct	GST = 0.40 × max(0, T - X_(allocated)) IRC §2601 (GST tax), §2055 (charitable deduction), §2632 (allocation).	Double	Engine shell
HELOC Calculatorheloc-calculator	Schedule	M_(draw) = P · i, M_(repay) = (P i)/(1-(1+i)^(-n)) HELOC structure — interest-only draw, then fully amortising repayment — under Regulation Z open-end credit rules (12 CFR §1026.40).	Double	Engine shell
Heston Volatility Calculatorheston-stochastic-volatility-surface-engine	Direct+ Solve	C = S e^(-qT) P_1 - K e^(-rT) P_2, P_j = (1)/(2) + (1)/(π)∫_0^(∞) Re [(e^(-iφ ln K) φ_j(φ))/(iφ)] dφ, dv_t = κ(θ - v_t) dt + ξ√(v_t) dW_t^(v), d W^S, W^v _t = ρ dt Heston (1993), "A Closed-Form Solution for Options with Stochastic Volatility and Applications to Bond and Currency Options", Review of Financial Studies 6(2), 327-343; Gatheral, The Volatility Surface (2006), for the P1/P2 decomposition and numerical integration.	Double	Engine bridge
HJM Interest Rate Calculatorheath-jarrow-morton-interest-rate-framework	Direct	df(t,T) = α(t,T) dt + σ(t,T) dW_t, α(t,T) = σ(t,T)∫_t^T σ(t,u) du, P(t,T) = exp (-∫_t^T f(t,u) du) Heath, D., Jarrow, R., & Morton, A. (1992), "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica 60(1), 77-105.	Double	Dedicated
Home Equity Loan Calculatorhome-equity-loan-calculator	Schedule	CLTV = (first + second)/(value) Lender CLTV policy, typically 85%, with level-payment amortisation for the second mortgage (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Home Sale Proceeds Calculatorhome-sale-proceeds-calculator	Direct	gain = P - C - (P_0 + I); taxable = max(0, gain - exclusion) IRC §121 for the primary-residence exclusion; IRC §1001 and §1016 for amount realised and adjusted basis.	Double	Engine shell
House Affordability Calculatorhouse-affordability-calculator	Directworker	L = PI·((1+r)^(n)-1)/(r(1+r)^(n)), Price = (L)/(1-d), PI = min(Gf, Gb - D) - T - I - H Inverted annuity-immediate loan sizing (Broverman, Mathematics of Investment and Credit); front- and back-end DTI conventions from US mortgage underwriting (28/36 conventional, 31/43 FHA, 41 VA). Computed with Big.js decimal arithmetic.	Big.js	Dedicated
Household Cash Flow Planhousehold-cash-flow-plan	Scheduleseeded	Net_t = (income_t + W_t + sale_t) - (spending_t + T_t) Cash-flow view of the deterministic household projection, net of sale costs and mortgage (Brigham & Ehrhardt, Financial Management, cash budgeting).	Double	Engine shell
Household Financial Planhousehold-financial-plan	Scheduleseeded	B_(t+1) = B_t(1+r) + S_t - W_t, W_t = spending_t + T_t Deterministic multi-year projection; tax from the 2025 federal brackets, drawdown order from the retirement tax engine.	Double	Engine shell
HSA Calculatorhsa-calculator	Schedule	B_(m+1) = B_m(1+(r)/(12)) + (c)/(12); saved = c (t + FICA) IRC §223 and IRS Rev. Proc. 2024-25 for the 2025 limits; the payroll exclusion follows IRC §125 cafeteria-plan treatment.	Double	Engine shell
Inflation Calculatorinflation-calculator	Direct	V_(real) = (V_(nom))/((1+π)^n), (1+r_(real)) = (1+r_(nom))/(1+π), r_(nom)^(*) = (π)/(1-t) Fisher (1930), "The Theory of Interest"; standard CPI deflation practice.	Double	Engine shell
Interest Rate Calculatorinterest-rate-solver	Solve	P(1+i)^n - M((1+i)^n - 1)/(i) = 0 Amortising loan balance equation solved for i by bisection (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Interest Rate Swap Calculatorinterest-rate-swap-calculator	Direct	Net = N(S - L), NPV = Net · (1-(1+r)^(-n))/(r) Single-curve swap valuation; break-even at the par swap rate.	Double	Engine shell
IRMAA and Medicare Premium Calculatorirmaa-medicare-calculator	Schedule	C_(yr) = 12 (P_B + S_D + P_D) CMS, 2026 Medicare Parts A & B Premiums and Deductibles fact sheet (14 November 2025).	Double	Dedicated
IRR Calculatorinternal-rate-of-return-solver-core	Solve	NPV(r) = Σ_(t=0)^(N) (CF_t)/((1+r)^t) = 0, MIRR = ((FV_(+))/(-PV_(-)))^(1/N) - 1 Brealey, Myers, and Allen, Principles of Corporate Finance — capital budgeting with NPV and IRR; modified IRR as presented in Chan S. Park, Contemporary Engineering Economics.	Double	Dedicated
IRRBB Calculatorirrbb-calculator	Direct	EVE = Σ (A_t)/((1+r_a)^t) - Σ (L_t)/((1+r_l)^t) BCBS (2016), Interest rate risk in the banking book, standardised framework and supervisory outlier test.	Double	Engine shell
Jump-Diffusion Option Calculatorjump-diffusion-merton-levy-process-engine	Direct	C = Σ_(n=0)^(∞) (e^(-λ' T)(λ' T)^(n))/(n!) C_(BS) (S,K,r_(n),σ_(n),T,q), λ' = λ(1+κ), κ = e^μ_J + (1)/(2)δ^(2) - 1, σ_(n)^(2) = σ^(2) + (nδ^(2))/(T), r_(n) = r - λκ + (nln(1+κ))/(T) Merton, R. C. (1976), "Option pricing when underlying stock returns are discontinuous", Journal of Financial Economics 3 (1–2), 125–144.	Double	Dedicated
Kelly Criterion Calculatorkelly-criterion-calculator	Direct	f^(*) = (p(b+1)-1)/(b), g(f) = pln(1+fb) + qln(1-f) Kelly (1956); Thorp (2006) on the Kelly criterion in markets.	Double	Engine shell
LBO Calculatorlbo-calculator	Direct	MOIC = (equity_(exit))/(equity_(entry)), IRR = MOIC^(1/t) - 1 Single entry, single exit IRR with no interim distributions or fund fees (Brealey, Myers & Allen, Principles of Corporate Finance).	Double	Engine shell
Life Insurance Needsinsurance-needs-calculator	Direct	— DIME needs analysis — debt, income, mortgage, education, less existing assets — the needs-based approach set out in the NAIC Life Insurance Buyer’s Guide.	Double	Dedicated
Loan Payment Calculatorloan-payment-calculator	Schedule	PMT = (P · i)/(1 - (1+i)^(-n)), i = (r)/(12), n = 12 · years, B_t = P(1+i)^t - PMT((1+i)^t - 1)/(i) Standard annuity-immediate amortisation formula; the APR is taken as a nominal annual rate compounded monthly (US consumer-loan payment convention). Reg Z Appendix J defines the disclosed actuarial APR, which includes finance charges.	Double	Engine shell
Local Volatility Calculatorlocal-volatility-calculator	Direct	σ^2(K,T) = (∂_T C + (r-q)K ∂_K C + qC)/( 12 K^2 ∂_(KK) C) Dupire (1994), Pricing with a Smile; Breeden & Litzenberger (1978) for the density identity.	Double	Engine shell
Long-Term Care Costltci-needs-calculator	Time march	— Inflated care costs against available assets and income, following the NAIC Shopper’s Guide to Long-Term Care Insurance.	Double	Dedicated
M&A Accretion / Dilutionmerger-accretion-dilution	Direct	— Pro forma EPS after synergies and financing cost (Brealey, Myers & Allen, Principles of Corporate Finance).	Double	Dedicated
Margin & Leverage Calculatormargin-liquidation-leverage-core	Direct	P_(liq)^(long) = P_0 (1-m_0)/(1-m), P_(liq)^(short) = P_0 (1+m_0)/(1+m), L = (Q P_0)/(Q P_0 m_0) US Federal Reserve Regulation T (initial margin) and FINRA Rule 4210 (maintenance margin); standard broker margin-account accounting.	Double	Dedicated
Market Microstructure Calculatorhigh-frequency-microstructure-signal-core	Direct	P^(μ) = (P^(a)V^(b) + P^(b)V^(a))/(V^(b) + V^(a)) = M + (S)/(2) I, M = (P^(a)+P^(b))/(2), S = P^(a)-P^(b), I = (V^(b)-V^(a))/(V^(b)+V^(a)), Δ p_t = λ q_t + ε_t, S_(Roll) = 2 max(-Cov(Δ p_t, Δ p_(t-1)), 0), RV = Σ_i r_i^2, BV = μ_1^(-2)Σ_i \|r_i\|\|r_(i-1)\| Kyle (1985), "Continuous Auctions and Insider Trading", Econometrica 53(6); Glosten & Milgrom (1985); Roll (1984), "A Simple Implicit Measure of the Effective Bid-Ask Spread"; Barndorff-Nielsen & Shephard (2004) for realized and bipower variation; Ait-Sahalia, Mykland & Zhang (2005) for the signature plot.	Double	Dedicated
Markup & Margin Calculatormarkup-margin-calculator	Direct	P = C(1+m), g = (P-C)/(P) = (m)/(1+m), P_(target) = (C)/(1-g) Standard retail pricing identity; margin-on-price convention used in gross-margin reporting (Horngren et al., Cost Accounting).	Double	Engine shell
Marriage Penalty Calculatormarriage-penalty-calculator	Direct	P = T_(MFJ)(a+b-D_(joint)) - [T(a-D_a) + T(b-D_b)] IRC §1(j) 2025 rate schedules and §164(b)(6) SALT cap; the standard deduction is §63(c).	Double	Engine shell
MBS Prepayment Calculatormbs-prepayment-calculator	Schedule	CPR(t) = 6%×min(t/30,1); SMM = 1-(1-CPR)^(1/12) Public Securities Association prepayment model; the WAL and passthrough conventions follow Fabozzi, Fixed Income Analysis.	Double	Engine shell
Monte Carlo Simulation Calculatormonte-carlo-stochastic-path-engine	Simulateseeded	S_(t+Δ t) = S_t exp((μ - (1)/(2)σ^2)Δ t + σ√(Δ t) Z), ln S_T ~ N(ln S_0 + (μ - (1)/(2)σ^2)T, σ^2 T) Hull, Options, Futures, and Other Derivatives (Wiener processes and Ito’s lemma); Glasserman, Monte Carlo Methods in Financial Engineering (2003) for path simulation and antithetic variates.	Double	Engine bridge
Mortgage Calculatormortgage-principal-calculus-engine	Schedule	M = P (r(1+r)^(n))/((1+r)^(n)-1), r = (APR)/(1200), n = months Standard annuity-immediate amortization formula (Broverman, Mathematics of Investment and Credit); the APR is taken as a nominal annual rate compounded monthly, the usual US consumer-loan payment convention. Reg Z Appendix J defines the disclosed actuarial APR.	Double	Engine shell
Mortgage Payoff Calculatormortgage-payoff-calculator	Scheduleworker	B_(k+1) = B_(k)(1+r) - (M + E), M = P (r(1+r)^(n))/((1+r)^(n)-1), r = (APR)/(1200) Annuity-immediate payment (Broverman, Mathematics of Investment and Credit); the accelerated path is simulated month by month with 20-significant-digit decimal arithmetic (Decimal.js), capping the final payment at the remaining balance.	Decimal.js	Dedicated
Mortgage Recast Calculatormortgage-recast-calculator	Direct	— Re-amortising the remaining balance over the original term (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
Mutual Fund Calculatormutual-fund-calculator	Time march	— Net return = gross return − expense ratio, compounded annually, per the SEC Form N-1A fee disclosure.	Double	Dedicated
Net Investment Income Taxniit-calculator	Direct	— IRC §1411; thresholds are statutory and not indexed for inflation.	Double	Dedicated
Net Worth Calculatornet-worth-calculator	Direct	net worth = Σ A - Σ L, liquid = (A_(cash) + A_(invest)) - Σ L Standard personal financial statement — assets at fair market value less liabilities (Brigham & Ehrhardt, Financial Management).	Double	Engine shell
NPV Calculatornpv-calculator	Direct+ Solve	NPV = -C_0 + Σ_(t=1)^(T) (CF_t)/((1+r)^t), 0 = -C_0 + Σ_(t=1)^(T) (CF_t)/((1+IRR)^t), PI = (Σ PV(inflows))/(C_0) Brealey, Myers & Allen, "Principles of Corporate Finance", ch. 5–6; Graham & Harvey (2001) survey of CFO hurdle-rate practice.	Double	Engine shell
Option Pool Dilutionoption-pool-dilution	Solve	— The pool is carved out before the round, per the NVCA model legal documents.	Double	Dedicated
Payback Period Calculatorpayback-period-calculator	Direct	PB = t^* + (\|CumCF_(t^)\|)/(CF_(t^+1)), CumCF_t = -C_0 + Σ_(i=1)^(t) CF_i Brealey, Myers & Allen, "Principles of Corporate Finance", ch. 5 (payback as a screening rule).	Double	Engine shell
Paycheck Calculatorpaycheck-calculator	Direct	net = G - G d - T (max(0, G - Gd - D)) - FICA - s(G - Gd) - 12p IRC §1 (2026 brackets, IRS Rev. Proc. 2025-32); IRC §3101 (FICA); IRS Publication 15 (2026), social-security wage base $184,500.	Double	Engine shell
Pension Calculatordefined-benefit-pension-projection-core	Direct	S_t = S_0(1+g)^(t), PBO = (a S_T (T+1) e^(-μ T))/((1+d)^(T)), Interest cost = d × PBO IAS 19 Employee Benefits and IAS 26 Accounting and Reporting by Retirement Benefit Plans; projected unit credit method (actuarial present value of accrued benefits).	Double	Dedicated
Personal Loan Calculatorpersonal-loan-calculator	Schedule	— Level payment amortisation M = P·i/(1 − (1+i)^−n) (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
PMI Calculatorpmi-calculator	Schedule	PMI_(annual) = L · r_(pmi), LTV = (L)/(V) Homeowners Protection Act: automatic termination at 78% LTV, cancellation on request at 80%.	Double	Engine shell
Portfolio Optimization Calculatormarkowitz-efficient-frontier-optimization-matrix	Matrix	σ_p^2(μ_p) = (Aμ_p^2 - 2Bμ_p + C)/(D), A = 1^( )Σ^(-1)1, B = 1^( )Σ^(-1)μ, C = μ^( )Σ^(-1)μ, D = AC - B^2 Markowitz, H. (1952), "Portfolio Selection", Journal of Finance 7(1); closed-form frontier constants following Merton (1972), "An Analytic Derivation of the Efficient Portfolio Frontier".	Double	Dedicated
Present Value Calculatorpresent-value-calculator	Direct	— Discounted cash flow with the discount factor 1/(1 + r/n)^(nt) (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
Property Pro Formaproperty-proforma	Schedule	NOI = EGI - opex, cap = (NOI)/(price) Standard real estate underwriting — NOI before capex, TI and leasing commissions (Appraisal Institute, The Appraisal of Real Estate).	Double	Engine shell
Property Tax Calculatorproperty-tax-calculator	Direct	tax = max(0, V · r - E) · (m)/(1000) Local assessment statutes; one mill equals $1 of tax per $1,000 of taxable value (IAAO, Property Appraisal and Assessment Administration).	Double	Engine shell
PSLF Calculatorpslf-calculator	Schedule	eligible = Direct employer full time plan certified 34 CFR 685.219, Public Service Loan Forgiveness Program.	Double	Engine shell
QBI Deduction (199A) Calculatorqbi-deduction-calculator	Direct	D = min(0.2 QBI, 0.2 TI, W) IRC §199A; IRS Rev. Proc. 2025-32 §3.26 for the 2026 thresholds.	Double	Dedicated
Quarterly Estimated Tax Calculatorquarterly-estimated-tax-calculator	Direct	T = Σ slice × rate; harbour = min(0.9 T, 1.0 or 1.1 T_(-1)) IRC §6654(d) for the safe harbours; brackets and the standard deduction from Rev. Proc. 2024-40; self-employment tax under §1401.	Double	Engine shell
Real Estate Investment Calculatorreal-estate-asset-yield-engine	Direct	R_0 = (NOI_1)/(V_0), PV = Σ_(t=1)^(n)(CF_t)/((1+Y)^(t)) + (TV_n)/((1+Y)^(n)), TV_n = (NOI_(n+1))/(R_(exit)) Appraisal Institute yield-capitalization and DCF conventions (The Appraisal of Real Estate); NCREIF definitions of NOI and cap rate; Gordon-growth alternative for terminal value.	Double	Dedicated
Refinance Calculatordebt-refinancing-arbitrage-matrix	Directworker	Break-even = (Closing costs)/(M_(old) - M_(new)), M = P (r(1+r)^(n))/((1+r)^(n)-1) Annuity-immediate payment formula (Broverman, Mathematics of Investment and Credit) with the APR treated as a nominal annual rate compounded monthly; break-even is fixed cost divided by periodic saving. Reg Z Appendix J governs the disclosed APR, which this model takes as an input rather than recomputing.	Decimal.js	Engine bridge
Regime-Switching Model Calculatorregime-switching-hamilton-markov-engine	Scheduleseeded	ξ_(t\|t-1) = P ξ_(t-1\|t-1), ξ_(t\|t) = (ξ_(t\|t-1) η_t)/(1^( )(ξ_(t\|t-1) η_t)), η_(t,j) = (1)/(√(2π)σ_j)exp (-((y_t-μ_j)^2)/(2σ_j^2)), log L = Σ_(t=1)^(T)log [1^( )(ξ_(t\|t-1) η_t)], E[duration_j] = (1)/(1-p_(jj)) Hamilton (1989), "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle", Econometrica 57(2), 357-384; Kim (1994) smoothing recursion; Hamilton, Time Series Analysis (1994), ch. 22.	Double	Dedicated
Rent Affordability Calculatorrent-affordability-calculator	Direct	rent = min(0.30 G_(m), G_(a)/40, N(1-s)-E-D) HUD defines housing above 30% of gross income as a cost burden and above 50% as severe; the 40× rule is the standard landlord screen.	Double	Engine shell
Rent vs Buy Calculatorrent-vs-buy-calculator	Schedule	C_(buy)(t) = D + K + Σ_(s=1)^(t)(M_s + carry_s) - benefit_t - E_t; C_(rent)(t) = Σ_(s=1)^(t) R_s - (D+K)[(1+i)^t-1] Net-cost comparison as set out in the NYT rent-versus-buy model and in Geltner & Miller, Commercial Real Estate Analysis; equity is measured net of selling costs.	Double	Engine shell
Retirement Calculatorretirement-calculator	Scheduleworker	B_(k+1) = (B_k + C_k)(1 + r_(pre)), B_(k+1) = (B_k - G_k)(1 + r_(post)), G_k = max (0, (I - S)(1+i)^(k)) Deterministic year-by-year accumulation with user-set returns (Broverman, Mathematics of Investment and Credit); Monte Carlo mode draws log-normal returns r = exp(mu − sigma²/2 + sigma·z) − 1 with z by Box-Muller.	Big.js	Dedicated
Retirement Plan Monte Carloretirement-plan-monte-carlo	Simulateseeded	r_t = μ + σ z_t, success = Pr[balance ≥ 0 t] Monte Carlo simulation with independent normal annual returns, replayed by the household projection engine on the accumulation identity (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Retirement Tax & Withdrawalretirement-tax-withdrawal	Schedule	RMD = (D)/(divisor(age)), T = Σ_i band_i × τ_i, W = max(0, S + T(W) - I) IRS Rev. Proc. 2024-40 and Rev. Proc. 2025-32 (2025 brackets and deductions); IRS Pub. 915 Worksheet 1 (taxable Social Security); Uniform Lifetime Table, Treas. Reg. §1.401(a)(9)-9; SECURE 2.0 RMD start age of 73.	Double	Engine shell
RMD Calculatorrmd-calculator	Schedule	RMD_t = (B_(t-1))/(D(age_t)); B_(t) = (B_(t-1) - RMD_t)(1+g) IRC §401(a)(9) and Treas. Reg. §1.401(a)(9)-9, Uniform Lifetime Table; applicable age from SECURE 2.0 §107.	Double	Engine shell
ROI Calculatorroi-calculator	Direct	ROI = ((V_(exit) + Income) - (Cost_0 + Costs))/(Cost_0 + Costs), r_(annual) = (1+ROI)^(1/n) - 1 Brigham & Ehrhardt, "Financial Management: Theory & Practice", ch. 11 (profitability measures).	Double	Engine shell
Roth IRA Calculatorroth-ira-calculator	Direct	FV = C((1+r)^n - 1)/(r), Roth: FV_R = FV(C), Traditional: FV_T = FV ((C)/(1-t_0))(1-t_1) IRC §408A (Roth IRA); standard tax-deferred equivalence argument.	Double	Engine shell
Rough Volatility Calculatorrough-volatility-fractional-brownian-core	Simulateseeded	v_t = ξ_0 exp (η B^(H)_t - (1)/(2)η^2 t^(2H)), Cov(B^(H)_t, B^(H)_s) = (1)/(2)(t^(2H) + s^(2H) - \|t-s\|^(2H)), E[v_t] = ξ_0, Var[v_T] = ξ_0^2(e^η^2 T^(2H) - 1) Gatheral, Jaisson & Rosenbaum (2018), "Volatility is Rough", Quantitative Finance 18(6), 933-949; Bayer, Friz & Gatheral (2016), "Pricing under Rough Volatility", for the rough Bergomi variance specification.	Double	Dedicated
RSU Calculatorequity-compensation-rsu	Direct	— Ordinary income at vest; flat supplemental withholding rate.	Double	Dedicated
SABR Swaption Calculatorstochastic-alpha-beta-rho-swaption-matrix	Direct	σ_B(K,F) = (α)/((FK)^((1-β)/2)[1 + ((1-β)^2)/(24)ln^2 (F)/(K) + ((1-β)^4)/(1920)ln^4 (F)/(K)])·(z)/(x(z))·1 + [((1-β)^2)/(24)(α^2)/((FK)^(1-β)) + (ρβνα)/(4(FK)^((1-β)/2)) + (2-3ρ^2)/(24)ν^2]T, z = (ν)/(α)(FK)^((1-β)/2)ln(F)/(K), x(z) = ln(√(1-2ρ z + z^2) + z - ρ)/(1-ρ) Hagan, Kumar, Lesniewski & Woodward (2002), "Managing Smile Risk", Wilmott Magazine, eqs. (2.17a-2.17c) for the implied-volatility smile and (2.18) for the at-the-money limit.	Double	Dedicated
Salary to Hourly Calculatorsalary-to-hourly-calculator	Direct	r_(pay) = (S - bonus)/(h_w · w); r_(eff) = (S_(total))/(h_w · w - h_(leave)) FLSA regular-rate definition (29 CFR §778.109) for the payslip rate; the effective rate is the same identity with hours actually worked as the denominator.	Double	Engine shell
Sales Tax Calculatorsales-tax-calculator	Direct	c = state + local, G = N(1+c), N = (G)/(1+c) State revenue codes; Streamlined Sales Tax sourcing conventions.	Double	Engine shell
Savings Calculatorsavings-calculator	Scheduleworker	B_(k+1) = B_k(1+r_m) + D, r_m = (1+(r_(net))/(m))^(m/12)-1, r_(net) = APY (1-t) Monthly-compounded future value with level deposits (compound interest combined with the future value of an annuity; Broverman, Mathematics of Investment and Credit). Doubling time uses the Rule-of-72 approximation 72 ÷ rate; the real value deflates the balance by (1 + inflation)^(years).	Double	Dedicated
Savings Goal Calculatorsavings-goal-calculator	Direct	PMT = ([FV - PV(1+i)^n] i)/((1+i)^n - 1), i = (r)/(12), n = 12t Standard sinking-fund formula (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Scenario DCF Valuation Calculatormulti-scenario-dcf-valuation-matrix	Direct	FCFF_t = NOPAT_t - CapEx_t - _t, EV = Σ_(t=1)^(n)(FCFF_t)/((1+WACC)^(t)) + (TV)/((1+WACC)^(n)), TV = (FCFF_(n)(1+g))/(WACC-g) Standard two-stage FCFF discounted-cash-flow valuation; Gordon (1959) growth model for terminal value; Damodaran, Investment Valuation, and Koller, Goedhart & Wessels, Valuation.	Double	Dedicated
Scenario Provision Calculatorscenario-provision-calculator	Direct	EL = Σ_i w_i · PD_i · LGD_i · EAD IFRS 9 / CECL multi-scenario expected credit loss.	Double	Engine shell
Self-Employment Tax Calculatorself-employment-tax-calculator	Direct	SECA = 12.4%·min(0.9235P, 176,100) + 2.9%·0.9235P IRC §1401 (SECA), 2025 Social Security wage base $176,100, IRS Schedule SE.	Double	Engine shell
Sequence-of-Returns Backtestsequence-of-returns-backtest	Schedule	B_t = B_(t-1)(1 + w r_(e,t) + (1-w) r_b - f) - W(1+π)^t Bengen (1994), “Determining Withdrawal Rates Using Historical Data”; Kitces on sequence-of-returns risk. Equity data: S&P 500 total return, 1926–2025.	Double	Engine shell
Series I Bond Calculatorseries-i-bond-calculator	Schedule	c = f + 2π + fπ; V_m = P(1 + (c)/(2))^(m/6) Treasury formula under 31 CFR Part 360; rates published by TreasuryDirect each May and November.	Double	Engine shell
Sharpe Ratio Calculatorsharpe-ratio-calculator	Direct	Sharpe = (R_p - R_f)/(σ_p), Sortino = (R_p - R_f)/(σ_(down)), Treynor = (R_p - R_f)/(β), α = R_p - [R_f + β(R_m - R_f)] Sharpe (1966, 1994); Sortino & Price (1994); Treynor (1965); Jensen (1968).	Double	Engine shell
Simple Interest Calculatorsimple-interest-calculator	Direct	I = P · r · t, A = P + I Simple interest with months converted to years (Broverman, Mathematics of Investment and Credit).	Double	Engine shell
Social Security Claiming Calculatorsocial-security-claiming-calculator	Schedule	Early benefit=PIA[1-min(m,36)(5)/(900)-max(m-36,0)(5)/(1200)], Delayed benefit=PIA(1+dc) SSA, Early or Late Retirement (https://www.ssa.gov/OACT/quickcalc/early_late.html); SSA, Annual Statistical Supplement 2025, Appendix C (https://www.ssa.gov/policy/docs/statcomps/supplement/2025/apnc.html); SSA, OASDI Program Reference, Tables 9–10 (https://www.ssa.gov/policy/about/oasdi-reference.html).	Double	Engine shell
State Estate Tax Calculatorstate-estate-tax-calculator	Direct	T = 0.40max(0, E - D - X_f) + r_smax(0, E - D - X_s) IRC §2001 (federal); state estate tax statutes differ and should be checked directly.	Double	Engine shell
State Income Tax Calculatorstate-income-tax-calculator	Schedule	T = Σ_i (I_i × r_i) Tax Foundation, 2026 State Individual Income Tax Rates and Brackets, compiled from state statutes.	Double	Dedicated
Student Loan Calculatorstudent-loan-calculator	Schedule	PMT = (B · i)/(1-(1+i)^(-n)), I_(total) = n · PMT - B, DTI = (12 · PMT)/(income) Federal Direct Loan standard repayment mechanics (34 CFR 685.208).	Double	Engine shell
Student Loan IDR Calculatorstudent-loan-idr-calculator	Schedule	M = (s (AGI - m FPL))/(12) 34 CFR 685.209 (PAYE, ICR, SAVE) and 685.221 (IBR), with the 2025 HHS poverty guidelines.	Double	Engine shell
Student Loan Refinance Calculatorstudent-loan-refinance-calculator	Schedule	net = (I_(current) - I_(new)) - F_(forfeited) Level-payment amortisation; the federal protections forfeited are 34 CFR 685 (IDR) and 685.219 (PSLF).	Double	Engine shell
Swap Curve Calculatorswap-curve-calculator	Schedule	DF_i = (1 - s_i Σ_(j<i) DF_j)/(1 + s_i), NPV = N(SΣ DF - (1 - DF_n)) Standard par-rate bootstrapping; single-curve swap valuation.	Double	Engine shell
Tax Return Analyzer (1040)tax-return-analyzer	Schedule	T = Σ_i (B_i r_i) + T_(LTCG) + T_(NIIT) - C IRS Rev. Proc. 2025-32 (2026 brackets and standard deduction).	Double	Dedicated
Tax-Loss Harvestingtax-loss-harvesting-calculator	Direct	— Immediate tax saving and the time value of the deferral, subject to the IRC §1091 wash-sale rule (30 days).	Double	Dedicated
Three-Statement Modelthree-statement-model	Schedule	— Income statement, cash flow and balance sheet from one set of drivers (Brigham & Ehrhardt, Financial Management).	Double	Dedicated
Tip Calculatortip-calculator	Direct	T = base× r, total = base + tax + T, each = (total)/(n) US service-tipping convention; state and local sales-tax schedules. The definition of a tip follows the FLSA tipped-employee rule at 29 CFR §531.	Double	Engine shell
Trade Execution Calculatoroptimal-execution-almgren-chriss-protocol	Direct	x(t) = X (sinh (κ (T - t) ))/(sinh(κ T)), κ = (λ σ^(2))/(η), min_(x) E(x) + λ V(x) Almgren, R. & Chriss, N. (2000/2001), "Optimal Execution of Portfolio Transactions," Journal of Risk 3(2), 5-39; the continuous-time hyperbolic-sine liquidation trajectory with linear temporary and permanent impact.	Double	Dedicated
Traditional IRA Calculatortraditional-ira-calculator	Schedule	D = C × [1 - (MAGI - a)/(b - a)] IRC §219(b)(5) contribution limits and §219(g) deductibility phase-out, at the 2025 amounts.	Double	Engine shell
Treasury Bill Calculatortreasury-bill-calculator	Direct	P = F(1 - d(n)/(360)), y_(inv) = (F-P)/(P)·(365)/(n) US Treasury bill auction conventions: bank-discount basis, actual/360.	Double	Engine shell
Treasury Futures Hedge Calculatortreasury-futures-hedge-calculator	Direct	N = (V · D_p)/(P · 1000 · D_f / CF) Duration-based hedge ratio for Treasury futures; conversion factor adjusts for the cheapest-to-deliver.	Double	Engine shell
UK Income Tax Calculatoruk-income-tax-calculator	Schedule	T = Σ_i r_i × min(income - PA, band_i) HMRC income tax rates and allowances 2025/26; NI Class 1 employee contributions; Pensions Act 2008 automatic enrolment.	Double	Engine shell
UK Mortgage Calculatoruk-mortgage-calculator	Schedule	— Repayment mortgage with a product fee (Broverman, Mathematics of Investment and Credit).	Double	Dedicated
UK VAT Calculatoruk-vat-calculator	Direct	VAT = net × r; net = (gross)/(1 + r) VAT Act 1994: s.2(1) standard rate, Schedule 7A reduced, Schedule 4 zero-rated.	Double	Engine shell
Unit Economics Calculatorstartup-unit-economics	Direct	LTV = (ARPA · GM)/(churn), payback = (CAC)/(ARPA · GM) Gross-profit LTV with constant churn, as the present value of a decaying perpetuity (Brealey, Myers & Allen, Principles of Corporate Finance).	Double	Engine shell
Unit Price Calculatorunit-price-calculator	Direct	u = (p)/(q), saving = (u_(dear) - u_(cheap))/(u_(dear)), waste = n/q q - n Unit-pricing disclosure rules (EU 98/6/EC; US state unit-pricing statutes).	Double	Engine shell
VA IRRRL Calculatorva-irrrl-calculator	Direct	recoupment = (closing costs + 0.005 × B)/(P_(old) - P_(new)) VA Pamphlet 26-7 Chapter 6; funding fee under 38 CFR 36.4313.	Double	Engine shell
VA Loan Calculatorva-loan-calculator	Schedule	F = r_(fee) × (P - D) VA Lender’s Handbook (VA Pamphlet 26-7), Chapter 8 for the funding fee; 2025 FHFA conforming limit of $806,500.	Double	Engine shell
Value at Risk (VaR) Calculatorvalue-at-risk-volatility-core	Simulate+ Directseeded	VaR_c = V_0 max(0, -(μ h + σ√(h) z_(1-c))), ES_c = V_0(-μ h + σ√(h) (φ(z_(1-c)))/(1-c)), σ_t^2 = λσ_(t-1)^2 + (1-λ) r_(t-1)^2 RiskMetrics Technical Document (J.P. Morgan, 1996) for the EWMA recursion with lambda = 0.94 on daily data; Basel Committee on Banking Supervision market-risk framework for VaR at 99% over 10 days; Hull, Options, Futures, and Other Derivatives (VaR and expected shortfall chapters).	Double	Engine bridge
VAT Calculatorvat-calculator	Direct	Add: G = N(1+r), VAT = Nr Remove: N = (G)/(1+r), VAT = G - N EU VAT Directive 2006/112/EC, Art. 73 (taxable amount inclusive of tax); national GST legislation follows the same algebra.	Double	Engine shell
WACC Calculatorwacc-calculator	Direct	K_e = r_f + β · ERP, WACC = (E)/(V)K_e + (D)/(V)K_d(1-T), V = E + D Modigliani & Miller (1958, 1963) — the after-tax WACC follows the 1963 tax correction; Damodaran, "Applied Corporate Finance", ch. 7–8.	Double	Engine shell
Working Capital and Cash Cycleworking-capital-cash-cycle	Direct	CCC = DIO + DSO - DPO DIO and DPO against COGS, DSO against revenue (Brigham & Ehrhardt, Financial Management, ratio analysis).	Double	Engine shell
XVA Calculatorxva-capital-calculator	Simulateseeded	FVA = s_f Σ EPE(t) DF(t) Δ t; KVA = k_e Σ K(t) DF(t) Δ t XVA framework: FVA/FBA (Albanese & Andersen), MVA and KVA as the cost of funding margin and capital.	Double	Engine shell

The output contract

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A number without its method is a claim. Each calculator publishes the same three things beneath the live result, so the arithmetic can be checked rather than trusted.

Formula

The exact relationship the page implements, typeset in KaTeX, with the textbook, standard or paper it is taken from. 322 of 372 calculators publish one.

Worked example

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Assumptions

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372 of 372 calculators carry published editorial content; 241 mount through the shared engine shell, 8 through an engine bridge and 123 as standalone pages. Counts are generated from the source tree by scripts/gen-calculation-methods.mjs and scripts/gen-calculation-architecture.mjs.

Method-level references for each domain are collected on the finance and engineering methodology pages.