How to Calculate Electrical Power (P = V × I)
Electrical power measures the rate at which a circuit converts electrical energy into another form — heat, light, or motion — and is measured in watts (W), where one watt equals one joule per second. The three quantities that describe a simple resistive circuit — voltage (V), current (I), and resistance (R) — are linked by Ohm's Law (V = IR), so knowing any two of them is enough to find power and the missing third quantity. This calculator lets you enter whichever pair you know and returns power along with voltage, current, and resistance.
The three power formulas
- P = V × I — use when voltage and current are known (the most direct measurement, e.g. readings from a multimeter).
- P = I² × R — use when current and resistance are known; this substitutes V = IR into P = VI.
- P = V² / R — use when voltage and resistance are known; this substitutes I = V/R into P = VI.
All three give the same answer for a given resistive circuit because they are algebraic rearrangements of the same two laws: Ohm's Law and P = VI.
Practical notes on power and heat
- Power dissipated as heat determines component ratings: a resistor or wire must be rated above the calculated wattage, with headroom (commonly 50–70% of rated capacity) to avoid overheating.
- Household appliances list power in watts on their nameplate; multiplying watts by hours of use and dividing by 1000 converts to kilowatt-hours (kWh) for utility billing.
- These formulas assume resistive (ohmic) loads. For AC circuits with reactive components (motors, capacitors, inductors), real power also depends on the phase difference between voltage and current — see a power factor calculator for that case.
- Zero or negative resistance and zero current in the voltage-and-current calculation are not physically meaningful here, since resistance is derived by dividing — the calculator flags these cases instead of returning a result.
Frequently Asked Questions
What is the formula for electrical power?
Electrical power equals voltage multiplied by current: P = V × I, measured in watts. When only two of the three circuit quantities (voltage, current, resistance) are known, the equivalent forms P = I²R and P = V²/R give the same result.
How do I find power when I only know current and resistance?
Use P = I² × R. This comes from substituting Ohm's Law (V = IR) into P = VI, so you never need to measure voltage directly.
How do I find power when I only know voltage and resistance?
Use P = V² / R. This comes from substituting I = V/R (Ohm's Law) into P = VI, so you never need to measure current directly.
What's the difference between watts and kilowatt-hours?
Watts measure the instantaneous rate of energy use (power), while kilowatt-hours measure total energy consumed over time — power multiplied by hours, divided by 1000. A 100 W bulb running for 10 hours uses 1 kWh of energy, not 100 kWh.