Ohm’s Law Calculator
Ohm's Law Calculator
Enter any two of voltage, current, resistance and power and get the other two, with units scaled automatically from µA to kA and mΩ to MΩ — plus the full wheel of twelve Ohm’s-law formulas.
Ohm's law: V, I, R and P
9 V across a resistor with 15 mA flowing through it
Ohm’s law and the power law
- V
- voltage across the component, in volts (V)
- I
- current through it, in amperes (A)
- R
- resistance, in ohms (Ω); 1 Ω = 1 V ÷ 1 A
- P
- power turned into heat in it, in watts (W); 1 W = 1 V × 1 A
Worked example
9 V across a resistor with 15 mA flowing through it
R = V ÷ I = 9 ÷ 0.015 = 600 Ω
P = V × I = 9 × 0.015 = 0.135 W = 135 mW
Check: P = I² × R = 0.015² × 600 = 0.135 W, and V² ÷ R = 81 ÷ 600 = 0.135 W
The defaults are the same point in every mode: choose any pair of 9 V, 15 mA, 600 Ω and 135 mW and the other two come back.
The Ohm’s law wheel: twelve formulas
| Find | Formula | Example: 9 V, 15 mA, 600 Ω, 135 mW |
|---|---|---|
| Voltage V | V = I × R | 9 V |
| Voltage V | V = P ÷ I | 9 V |
| Voltage V | V = √(P × R) | 9 V |
| Current I | I = V ÷ R | 15 mA |
| Current I | I = P ÷ V | 15 mA |
| Current I | I = √(P ÷ R) | 15 mA |
| Resistance R | R = V ÷ I | 600 Ω |
| Resistance R | R = V² ÷ P | 600 Ω |
| Resistance R | R = P ÷ I² | 600 Ω |
| Power P | P = V × I | 135 mW |
| Power P | P = I² × R | 135 mW |
| Power P | P = V² ÷ R | 135 mW |
Using Ohm’s law
Ohm’s law says the current through a resistor is proportional to the voltage across it: V = I × R. Put 9 V across 600 Ω and 15 mA flows; double the voltage and the current doubles. The power law adds the fourth quantity: the power a component turns into heat is P = V × I. Substituting one law into the other gives the rest of the wheel, P = I² × R and P = V² ÷ R, so any two of the four quantities fix the other two. That is all this calculator does, but it handles the units for you: enter 15 mA or 0.015 A, 4.7 kΩ or 4,700 Ω, and the results come back scaled to µA, mA, kΩ or MΩ as they fall.
Power is the number people forget. A resistor has a power rating as well as a value. A 1 kΩ resistor across 12 V passes 12 mA and dissipates 144 mW: fine for a ¼ W part, though it will run warm. Choose a rating at least twice the dissipation you calculate, because ratings are given at a stated ambient temperature (often 70 °C) and fall above it. The same arithmetic runs a 2 kW, 230 V heater element: I = P ÷ V = 8.696 A and R = V² ÷ P = 26.45 Ω when hot.
Where it applies. Ohm’s law describes resistors and anything that behaves like one at a given moment. For AC it holds with RMS values when the load is purely resistive; capacitors and inductors add reactance, and power then depends on the phase angle. Diodes, LEDs and lamps are not ohmic: their resistance changes with the current, so V ÷ I at one point says nothing about another. A filament lamp’s cold resistance is several times lower than its hot resistance, which is why it draws a surge at switch-on. For an LED, use the LED resistor calculator; to split a voltage with two resistors, the voltage divider calculator; to read a resistor’s value from its bands, the resistor colour code calculator.
Frequently asked questions
What is Ohm’s law?
The voltage across a resistor equals the current through it times its resistance: V = I × R. Rearranged, I = V ÷ R and R = V ÷ I.
How do I calculate power from voltage and current?
Multiply them: P = V × I. 9 V and 15 mA give 0.135 W, or 135 mW. With resistance instead, use P = I² × R or P = V² ÷ R.
How do I work out the resistance I need?
Divide the voltage across the resistor by the current you want through it: R = V ÷ I. 9 V at 15 mA needs 600 Ω; the nearest standard values are 560 Ω and 620 Ω (E24).
Does Ohm’s law work for LEDs and diodes?
No. Their current rises steeply once the forward voltage is reached, so they have no fixed resistance. Apply Ohm’s law to the series resistor only, using the voltage left over after the LED’s forward voltage.
Does Ohm’s law work for AC?
For a purely resistive load, yes, with RMS voltage and current. With capacitors or inductors the opposition to current is an impedance that depends on frequency, and real power is less than V × I.
Related calculators
References
- Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. Chapter 1: voltage, current and resistance; Ohm’s law; power in resistors; voltage dividers and Thévenin equivalents.
- BIPM. The International System of Units (SI Brochure), 9th ed., 2019. Coherent derived units: the ohm (Ω = V/A) and the watt (W = J/s = V·A).