How to Calculate Electrical Power: P = VI Explained

Electrical power is how fast a circuit uses energy, and it's one of the most tested concepts in first-year engineering. The good news: there are three formulas, and they're all the same formula wearing different hats.

The three formulas

P = V × I = V² ÷ R = I² × R

P is power in watts, V is voltage in volts, I is current in amps, R is resistance in ohms. Which one you use depends on which two quantities you know — they're interchangeable through Ohm's law (V = I × R).

Worked example

A 9 V battery drives a 470 Ω resistor. What power does the resistor dissipate?

• Current first: I = V ÷ R = 9 ÷ 470 = 0.0191 A (19.1 mA)
• Then power: P = V × I = 9 × 0.0191 = 0.172 W (172 mW)

Alternatively, straight to P = V² ÷ R = 81 ÷ 470 = 0.172 W. Same answer, one fewer step.

Why the resistor rating matters

That 172 mW has to go somewhere — it becomes heat. A resistor rated ¼ W (250 mW) handles it fine, but a ⅛ W (125 mW) part would overheat and drift out of tolerance. Rule of thumb: use a resistor rated at least double the dissipated power.

Power vs. energy

Power is a rate (watts). Energy is power × time (watt-hours or joules) — what your electricity bill charges for. If you need cost or kWh, that's the electrical energy calculation.

Do the math instantly with the Power Calculator, then convert to kWh and cost with the Electrical Energy Calculator.