Three ways to the same power, depending on what you know
Power is how fast a circuit uses energy, measured in watts. Ohm's law (V = I × R) lets you swap between voltage, current and resistance, so power has three equivalent forms. Pick the one that matches the two values you already have.
- Know volts and amps → P = V × I. A device on 120 V drawing 5 A uses 600 W.
- Know amps and resistance → P = I² × R. Useful for wire heating: doubling the current quadruples the loss.
- Know volts and resistance → P = V² ÷ R. Handy for heaters and bulbs rated by voltage.
From power to energy: watts × time
Power tells you the rate; energy is the total once you add time. Multiply watts by seconds for joules, or watts by hours for watt-hours (the unit your electric bill uses, as kilowatt-hours).
| Device | Power | Run time | Energy used |
|---|---|---|---|
| LED bulb | 10 W | 1 hour | 36,000 J = 0.01 kWh |
| Laptop | 60 W | 1 hour | 216,000 J = 0.06 kWh |
| Microwave | 1,000 W | 5 min | 300,000 J = 0.083 kWh |
| Space heater | 1,500 W | 2 hours | 3 kWh |
One kilowatt-hour is 3,600,000 joules (1,000 W × 3,600 s). At a typical US rate near 17 cents/kWh, the space heater above costs about 51 cents to run.
Real power vs. apparent power on AC
On AC, multiplying volts by amps gives apparent power (volt-amps). The energy actually consumed is the real power, which is smaller whenever the load has coils or capacitors that shift the current out of phase.
- Resistive loads (heaters, kettles, incandescent bulbs) have PF = 1, so real power equals V × I.
- Motors run around PF 0.7–0.85; fluorescent lighting 0.5–0.9. A 1,000 VA motor at PF 0.8 draws only 800 W of real power.
- Wire losses follow I² × R, which is why long or thin cables warm up and why utilities push high voltage to keep current low.
Common questions
What is the difference between watts and joules?
A watt is a rate: one joule of energy every second. A joule is a fixed amount of energy. So a 60-watt bulb uses 60 joules each second, and energy in joules equals watts multiplied by the number of seconds.
How do I find power if I only know voltage and resistance?
Use P = V squared divided by R. For 120 volts across a 60-ohm heater, that is 14400 divided by 60, which is 240 watts. You do not need to know the current first.
Does this work for household AC power?
For resistive loads like heaters, kettles and incandescent bulbs, yes. For motors, LED drivers and anything with coils or capacitors, the real power is V times I times the power factor, which is less than the volts-times-amps figure.
