Ohm's Law Formulas: Volts, Amps, Ohms and Watts With Examples
Part of the project planner: Sizing a circuit: watts, amps, wire and breaker.
Ohm's law: V = I × R. Voltage (volts) equals current (amps) times resistance (ohms). Power is P = V × I, so any two of volts, amps, ohms and watts give the other two. Ten amps at 120 volts is 12 ohms and 1,200 watts. The Ohm's law calculator does it for any pair.
The twelve formulas
| To find | From V and I | From I and R | From V and R | From P and one other |
|---|---|---|---|---|
| Volts (V) | — | I × R | — | P ÷ I or √(P × R) |
| Amps (I) | — | — | V ÷ R | P ÷ V or √(P ÷ R) |
| Ohms (R) | V ÷ I | — | — | V² ÷ P or P ÷ I² |
| Watts (P) | V × I | I² × R | V² ÷ R | — |
Worked examples
| You know | Result |
|---|---|
| 120 V and 10 A | 12 Ω and 1,200 W |
| 12 V and 4 Ω | 3 A and 36 W |
| 2 A and 50 Ω | 100 V and 200 W |
| 120 V and 1,500 W | 12.5 A and 9.6 Ω |
| 5 A and 600 W | 120 V and 24 Ω |
| 100 W and 144 Ω | 120 V and 0.833 A |
Heaters on 120 V
Resistance and current of resistive heaters:
| Power | Current | Resistance |
|---|---|---|
| 500 W | 4.17 A | 28.8 Ω |
| 750 W | 6.25 A | 19.2 Ω |
| 1,000 W | 8.33 A | 14.4 Ω |
| 1,500 W | 12.50 A | 9.6 Ω |
| 1,800 W | 15.00 A | 8.0 Ω |
| 2,000 W | 16.67 A | 7.2 Ω |
Things to remember
- The unit prefixes matter: 1 kΩ is 1,000 Ω, and 1 mA is 0.001 A.
- Power rises with the square of the current or the voltage: doubling the current through a resistor gives four times the heat.
- Ohm's law is exact for a resistor. A lamp filament is much lower in resistance cold than hot, so a bulb draws a surge when it is switched on.
- For AC loads with a power factor below 1, the real power is V × I × power factor. See the watts to amps calculator.
Electricity is dangerous. Use this for learning and planning, and have a licensed electrician do household wiring.
Frequently asked questions
What is Ohm's law?
Voltage equals current times resistance: V = I × R. With the power formula P = V × I it links volts, amps, ohms and watts: any two give the others.
How do you calculate amps from volts and ohms?
Divide the volts by the ohms. 12 V across 4 Ω is 3 A.
How do you calculate resistance from watts and volts?
R = V² ÷ P. A 1,500 W heater on 120 V is 120² ÷ 1,500 = 9.6 Ω.
How do you calculate watts from amps and ohms?
P = I² × R. 2 A through 50 Ω is 200 W.
Does Ohm's law work for AC?
Yes for resistive loads such as heaters. For motors and electronics the power factor matters too, because current and voltage are out of step.
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