Electrical power, measured in watts, tells you how fast a device uses energy. One watt is one joule per second. Three formulas give power from different pairs of known values, and picking the right one is just a matter of what you already know.
The three formulas
P = V x I: power equals voltage times current. P = I squared x R: power equals current squared times resistance. P = V squared / R: power equals voltage squared divided by resistance. All three are the same law rearranged with Ohm’s law, so they always agree when the inputs are consistent.
Units: P in watts, V in volts, I in amps, R in ohms. For kilowatts, divide watts by 1,000. A 1,150-watt heater is 1.15 kW.
Worked examples
Mains appliance: 230 volts x 5 amps = 1,150 watts. Run for 2 hours, it uses 2.3 kWh of energy. Heater from current and resistance: 3 amps through 10 ohms gives P = 9 x 10 = 90 watts. Circuit from voltage and resistance: 12 volts across 6 ohms gives P = 144 / 6 = 24 watts, and the current is 12 / 6 = 2 amps, which cross-checks: 12 x 2 = 24 watts.
The cross-check habit catches errors fast. If P = V x I and P = I squared x R disagree, one of your inputs is wrong, usually a unit conversion or a resistance measured on the wrong part of the circuit.
DC versus AC
For DC circuits and for purely resistive AC loads like heaters and incandescent bulbs, P = V x I works directly with the ordinary voltage and current values. For AC circuits with motors, coils, or capacitors, part of the apparent power does no useful work, and real power is P = V x I x power factor. The power factor is a number between 0 and 1; a motor might run at 0.85.
Example: a motor drawing 10 amps at 230 volts with a 0.85 power factor uses 230 x 10 x 0.85 = 1,955 watts of real power, while the apparent power is 2,300 volt-amps. Sizing a supply or breaker from real power alone would undersize it, so use apparent power for supply sizing.
Choosing cables and fuses
Power tells you the current, and current tells you the cable and fuse size. A 2,300-watt appliance on 230 volts draws 10 amps, so it needs a circuit rated above 10 amps with margin. Never size a fuse exactly at the running current: start-up surges, especially motors, briefly draw several times more. Use the device manual and local wiring rules for final sizing.
Power versus energy
Power and energy are different quantities, and confusing them causes real billing errors. Power, in watts, is the rate of use at a moment. Energy, in watt-hours or kilowatt-hours, is power multiplied by time. A 1,150-watt heater running for 3 hours uses 1,150 x 3 = 3,450 watt-hours, or 3.45 kWh.
At $0.17 per kWh, that session costs 3.45 x 0.17 = $0.59. The same heater running for 30 minutes costs a tenth of the 3-hour session in energy, even though its power never changed. When comparing appliances, compare energy for the job, not power alone: a powerful appliance used briefly can cost less than a weak one left on all day.
Try it faster with the tool
You can follow every step above by hand, but the free Online Power Calculator does the arithmetic for you. Enter your numbers and it gives the answer right away, so you can check your hand calculation or skip straight to the result.
Quick tips
- P = V x I = I squared x R = V squared / R.
- For AC motors, multiply by the power factor for real power.
- Cross-check with a second formula to catch input errors.