Airfoil Lift & Drag Calculator
Calculate NACA airfoil lift, drag and moment coefficients, zero-lift angle and critical Mach for any angle of attack, Reynolds number and Mach number. Free.
NACA section geometry (Angle: 4° )
Section Geometry
Aerodynamic Calculations
A clear path from inputs to results.
Estimate the section lift, drag, and moment coefficients of a NACA airfoil at a chosen angle of attack, Reynolds number, and Mach number. It builds the airfoil from the 4-digit, 5-digit, or 6-series definitions, finds the zero-lift angle from thin-airfoil theory, and shows the lift curve, drag polar, and surface pressure distribution. It is a learning and preliminary-design tool for students, model builders, and engineers who want quick section-level numbers before running a full CFD or wind-tunnel study.
How to use
- Pick a preset (NACA 0012, 2412, 4415, 23012, or a 6-series) or choose a camber family and set the shape by hand.
- For a 4-digit section set the maximum camber (m) and its chordwise location (p); for 5-digit and 6-series set the design lift coefficient and mean-line parameters.
- Set the section thickness ratio and choose a closed or finite trailing edge.
- Set the flight condition: angle of attack (α), Reynolds number (Re), and Mach number (M).
- Read the section lift (Cl), drag (Cd), zero-lift angle (α₀), and critical Mach (Mcr) in the summary tiles.
- Switch tabs to inspect the airfoil silhouette, the surface pressure (−Cp) distribution, and the lift and drag polars.
The formula
Reference: Thin-airfoil theory: Anderson, Fundamentals of Aerodynamics (6th ed.), Ch. 4; zero-lift angles tabulated in Abbott & von Doenhoff, Theory of Wing Sections.
Worked example
NACA 2412 at 4° angle of attack
- NACA 2412 (2% camber at 40% chord, 12% thick), closed trailing edge; angle of attack α = 4°; Reynolds number Re = 3,000,000; Mach M = 0.25.
- 1
The camber mean-line slope is integrated by thin-airfoil theory to give the zero-lift angle α_L0 = −(1/π)∫(dz/dx)(cos θ₀ − 1) dθ₀ = −2.077°, matching the Abbott & von Doenhoff value for the NACA 2412. The lift-curve slope is 2π(1 + 0.77·0.12) = 6.864 per radian, so the incompressible lift is 6.864 × (4 − (−2.077)) × π/180 = 0.728. A Prandtl-Glauert correction divides by √(1 − 0.25²) = 0.9682, giving Cl = 0.752. At α = 0° the same relation gives Cl = 6.864 × 2.077 × π/180 ÷ 0.9682 = +0.257 — positive lift for a positively cambered section, as expected. Drag combines a skin-friction profile term Cd₀ = 0.004134 with a lift-dependent penalty 0.007 × (|Cl − Cl_design| − 0.05)² = 0.003160; since M = 0.25 is below the critical Mach Mcr ≈ 0.677 there is no wave drag, so Cd = (0.004134 + 0.003160)(1 + 0.1·0.25²) = 0.007340.
Cl ≈ 0.752, Cd ≈ 0.00734 (lift-to-drag ratio ≈ 102), quarter-chord moment Cm ≈ −0.195, zero-lift angle α₀ = −2.077°, critical Mach ≈ 0.677.
Interpreting the result
The zero-lift angle is negative for a cambered airfoil, so the section already produces lift at 0° — read Cl off the lift line relative to α₀, not relative to 0°. Cl rises roughly linearly at about 2π per radian (0.11 per degree) until the curve bends over near stall. Drag is smallest in the "bucket" around the design lift coefficient and climbs steeply once the Mach number passes the critical value and wave drag appears.
Assumptions & limitations
- Thin-airfoil theory assumes small camber, small thickness, and small angles with fully attached, inviscid flow; it is a preliminary estimate, not a stall or separation prediction.
- The lift-curve slope uses an empirical thickness correction 2π(1 + 0.77 t) rather than a strict 2π, and compressibility is handled by a simple Prandtl-Glauert factor valid only in subsonic flow.
- Drag is a simplified flat-plate skin-friction model with a quadratic laminar-bucket penalty and a crude wave-drag rise past the critical Mach number; it is not a boundary-layer or transition solver.
- The stall roll-off and critical-Mach estimates are empirical fits, so results near and beyond stall or near Mach 1 are indicative only.
- Three-dimensional effects (finite wings, sweep, downwash) are not modeled; outputs are two-dimensional section coefficients per unit span.
Frequently asked questions
Why is the zero-lift angle negative for a cambered airfoil?
Positive camber bends the mean line so the section already generates lift when the chord line is horizontal. To reach zero lift you must pitch the nose down to a negative angle. Thin-airfoil theory gives α_L0 = −(1/π)∫(dz/dx)(cos θ₀ − 1) dθ₀, which comes out to about −2.077° for the NACA 2412 — exactly the value tabulated by Abbott & von Doenhoff.
How is the lift coefficient calculated?
The tool uses the thin-airfoil result Cl = 2π(α − α_L0), with a small empirical thickness correction to the slope and a Prandtl-Glauert factor for compressibility. The slope is about 2π per radian, or roughly 0.11 per degree, until the empirical stall model bends the curve over.
Which NACA families can I model?
You can model 4-digit sections (set camber and its location), 5-digit sections such as the 23012 (set the design lift coefficient and mean-line position, with an optional reflex), and 6-series laminar sections (set the design lift coefficient and the uniform-load fraction a). Thickness and trailing-edge closure are adjustable in every family.
What lift does a NACA 2412 make at 0° angle of attack?
Because its zero-lift angle is −2.077°, a NACA 2412 at 0° is effectively at +2.077° relative to its zero-lift line, giving a positive section lift coefficient of about 0.26 at M = 0.25 in this tool. A symmetric section such as the NACA 0012 makes exactly zero lift at 0°.
What is the critical Mach number shown in the results?
The critical Mach number (Mcr) is the free-stream Mach at which the flow first reaches the speed of sound somewhere on the airfoil. Above it, shock waves form and wave drag rises sharply. The tool estimates Mcr from thickness and lift and adds a wave-drag term once the operating Mach exceeds it.
Can I use these numbers for a real wing design?
Use them for learning and early trade studies. These are two-dimensional section coefficients from simplified theory; a real wing adds finite-span downwash, sweep, surface roughness, and viscous separation. Validate any design-critical numbers against a viscous panel code, CFD, or wind-tunnel data.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.