Skip to content

    Under active development. New calculators and features ship every week. Everything currently runs free while the site matures — pricing pages are a preview, checkout is not open yet.

    Search ⌘K
    Engineering / Ohm's Law (V, I, R, P)

    Ohm's Law Calculator — V, I, R, P

    Solve voltage, current, resistance and power from any two knowns, plus appliance energy cost and battery runtime in the same tool.

    ToolCalculatorExecutionIn browserCategoryEngineering
    OHM
    COST
    BATT
    ⚙
    ZORVLABS
    SYSTEM STATUS
    GRID SYNC: STABLE
    CIRCUIT PARAMETERS
    OHM'S LAW
    ENERGY
    BATTERY
    Enter any 2 values to calculate rest:
    VOLTAGE (V)
    CURRENT (I)
    RESISTANCE (R)
    POWER (P)
    CIRCUIT SIMULATION
    FLOW: IDLE
    DISSIPATION METRICS
    ANALYTICAL OUTPUT
    0.00
    UNITS
    EFFICIENCY RATING
    N/A
    engineering methodology

    A clear path from inputs to results.

    Ohm's law and the power equation together give four quantities from any two. This calculator solves that system, then applies it to the two questions people actually ask: what does this appliance cost to run, and how long will this battery last.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter any two of voltage, current, resistance or power; the remaining two are solved.
    2. Check the unit prefixes — mA and mW are handled automatically.
    3. Switch to the cost mode to price an appliance from its wattage and hours of use.
    4. Switch to the battery mode to estimate runtime from capacity, voltage and load current.
    5. Read the derived values and the efficiency readout for the entered load.

    The formula

    V=IR,P=VI=I2R=V2R,cost=P t1000×tariffV = IR, \qquad P = VI = I^2R = \frac{V^2}{R}, \qquad \text{cost} = \frac{P\,t}{1000}\times \text{tariff}

    Reference: Ohm's law; Joule's law; standard DC circuit analysis.

    Worked example

    12 V across 4 Ω

    Inputs
    • Voltage 12 V.
    • Resistance 4 Ω.
    Calculation path
    1. 1

      Current: I = V/R = 12/4 = 3 A.

    2. 2

      Power: P = VI = 12 × 3 = 36 W.

    3. 3

      Cross-check: I²R = 9 × 4 = 36 W. ✓

    4. 4

      A 1,000 W appliance run 24 h at $0.15/kWh costs 24 × 0.15 = $3.60.

    5. 5

      A 3,000 mAh 3.7 V battery at 500 mA gives about 6 hours of nominal runtime.

    Result

    3 A and 36 W from 12 V across 4 Ω; 1 kW for a day costs $3.60.

    Interpreting the result

    The four quantities are not independent — two determine the other two, which is why entering three and expecting a consistent answer is a common source of error. The battery runtime is a nominal figure: real cells lose capacity at high discharge rates and low temperature, so treat it as an upper bound.

    Assumptions & limitations

    • DC or purely resistive AC. Reactive loads need impedance, not resistance.
    • The source is ideal with zero internal resistance.
    • Battery capacity is taken at face value; Peukert effects reduce usable capacity at high current.
    • Energy cost uses a flat tariff with no standing charges or time-of-use bands.

    Frequently asked questions

    Can I enter all four values?

    No — they are constrained by two equations, so the fourth would generally be inconsistent. Enter any two and let the calculator solve the rest.

    How accurate is the battery runtime?

    It is a first-order estimate. Capacity falls with discharge rate (Peukert), temperature and age, so expect the real runtime to be 60–80% of the nominal figure.

    Why does my measured current differ from the calculation?

    Because the source has internal resistance, the wiring has resistance, and the load changes with temperature. A 12 V nominal supply often measures 11.5 V under load.

    Does this work for AC?

    For a purely resistive AC load, yes — the RMS values behave the same way. For motors and transformers you need impedance and power factor, which is a different calculation.

    Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.