Three formulas, one for whatever two values you have
Electrical power is watts. Which formula you use depends on which two of voltage, current and resistance you know. The first covers almost every real case; the other two come from Ohm's law for when resistance is the value in hand.
- P = V × I. Volts times amps. Use this when you know the supply voltage and the current drawn.
- P = I² × R. Use when you know the current and the resistance, common for heating elements and cable losses.
- P = V² ÷ R. Use when you know the voltage across a component and its resistance.
Rearranging to solve for any variable
Once you have power, the same relationship gives you the missing input. These are just P = V x I flipped around.
| Solve for | Formula | Example |
|---|---|---|
| Power | P = V × I | 120 V × 10 A = 1,200 W |
| Current | I = P ÷ V | 1,200 W ÷ 120 V = 10 A |
| Voltage | V = P ÷ I | 1,200 W ÷ 10 A = 120 V |
| Resistance | R = V² ÷ P | 120² ÷ 1,200 = 12 Ω |
Common wattages and horsepower conversions
| Watts | kW | HP (mechanical) | BTU/h |
|---|---|---|---|
| 100 W | 0.1 | 0.134 | 341 |
| 746 W | 0.746 | 1.00 | 2,545 |
| 1,000 W | 1.0 | 1.34 | 3,412 |
| 1,500 W | 1.5 | 2.01 | 5,118 |
| 5,000 W | 5.0 | 6.71 | 17,060 |
One mechanical horsepower is 745.7 W; metric horsepower (PS) is 735.5 W, about 1.4% less. To go from HP to kW, multiply by 0.746.
Where the calculation goes wrong
- Watts are not watt-hours. A watt is the rate of energy use right now; a watt-hour is the total after time. A 100 W bulb on for 5 hours uses 500 Wh, or 0.5 kWh.
- Nameplate is not actual draw. A fridge rated 250 W does not pull 250 W constantly; the compressor cycles on and off, so real consumption is much lower.
- Watts vs VA. On motors and fluorescent gear the real power in watts is below the apparent power in volt-amps. They only line up on purely resistive loads.
Common questions
How do I calculate watts from volts and amps?
Multiply voltage by current: watts = volts x amps. A device drawing 10 amps at 120 volts uses 1,200 watts. This is the everyday formula for electrical power.
How do I find watts when I only know current and resistance?
Use P = I squared x R. Square the current in amps, then multiply by resistance in ohms. For 2 amps through 50 ohms: 2 x 2 x 50 = 200 watts.
Are watts and volt-amps (VA) the same thing?
Not for motors and other inductive loads. Watts are real power, the energy actually doing work. VA is apparent power. They match on simple resistive loads like heaters, but on a motor the watts are lower than the VA by the power factor.
How do I solve for voltage or current from watts?
Rearrange P = V x I. Voltage equals power divided by current (V = P / I), and current equals power divided by voltage (I = P / V). A 1,200 watt appliance on 120 volts draws 10 amps.
