Electric Power Calculator

Last updated: 2026-05-18

What is electric power?

Electric power is the rate at which a circuit converts electrical energy into another form, such as heat, light, or mechanical work. It is measured in watts (W), where one watt equals one joule of energy per second. The same power can be expressed through three equivalent formulas — P = V × I, P = I² × R, and P = V² ÷ R — each combining a different pair of the three Ohm's-law quantities: voltage (V), current (I), and resistance (R). This calculator evaluates all three at once, so the formula matching the two quantities that were actually measured is available without needing to know the third.

The three electric power formulas

The three formulas are equivalent whenever Ohm's law (V = I × R) holds. Each is the most direct choice for a different pair of known quantities.

Formula	When to use	Example
P = V × I	You know voltage and current	Outlet: 120 V × 2 A = 240 W
P = I² × R	You know current and resistance	Resistor: (3 A)² × 50 Ω = 450 W
P = V² ÷ R	You know voltage and resistance	Heater: (230 V)² ÷ 1000 Ω = 52.9 W

Why there are three formulas

Any two of Ohm's law quantities (V, I, R) determine the third, so three formulas cover all six combinations of two-of-three. Engineers choose the one that uses the two quantities they can actually measure. In circuit design, resistance is often known from components; in field measurement, voltage and current are read from a meter.

When inputs are inconsistent

When the three inputs do not satisfy V = I × R, the three power values disagree. The disagreement is informative rather than an error: it isolates which measured pair the result should rely on.

Example: V = 120, I = 3, R = 60 (inconsistent: 3 × 60 = 180 ≠ 120)

P_VI = 120 × 3 = 360 W (the value for a measured V and I)
P_I²R = 9 × 60 = 540 W (the value for a measured I and R)
P_V²R = 14400 ÷ 60 = 240 W (the value for a measured V and R)

Worked example: household appliances

A US household 120 V circuit has a 60 W light bulb. What current does it draw, and what is its resistance?

From P = V × I: I = P ÷ V = 60 ÷ 120 = 0.5 A
From V = I × R: R = V ÷ I = 120 ÷ 0.5 = 240 Ω

Check: P = V² ÷ R = 14400 ÷ 240 = 60 W ✓

From watts to energy cost

Power (watts) × time (hours) = energy (watt-hours). Divide by 1,000 for kilowatt-hours (kWh), which is what electricity bills charge:

\text{Cost} = \frac{P \times t}{1{,}000} \times \text{rate (per kWh)}

A 1,500 W space heater running 8 hours per day for 30 days uses:

\frac{1{,}500 \times 8 \times 30}{1{,}000} = 360 \text{ kWh}

At $0.15/kWh that costs $54 per month — a useful estimate before buying.

Frequently Asked Questions (FAQ)

What is the formula for electric power?

Electric power has three equivalent forms depending on which quantities are known: P = V × I (voltage times current), P = I² × R (current squared times resistance), and P = V² ÷ R (voltage squared divided by resistance). All three are equivalent when Ohm's law (V = I × R) holds, meaning the inputs are consistent. When V, I, and R are all entered, each formula gives the same result only if they satisfy Ohm's law.

How do I calculate watts from volts and amps?

Multiply voltage by current: P = V × I. For example, a 120 V circuit drawing 2 A uses 240 W. A 12 V car battery powering a 60 W load draws 60 ÷ 12 = 5 A. This is the most direct formula when both voltage and current are measurable.

What is the difference between P=VI and P=I²R?

They are mathematically identical when V = I × R. The difference is which two quantities are already known. P = V × I applies when voltage and current are known, P = I² × R when current and resistance are known (but not voltage), and P = V² ÷ R when voltage and resistance are known. If the three inputs are inconsistent with Ohm's law, the three formulas give different results, which isolates the input pair that was actually measured.

How do I convert watts to kilowatt-hours?

Energy (kWh) = Power (kW) × Time (h). A 240 W device running for 5 hours uses 0.24 kW × 5 h = 1.2 kWh. Electricity bills are priced per kWh, so multiply kWh by the rate (typically $0.10–0.30/kWh in the US) to get cost. A 1,000 W (1 kW) device running for 1 hour consumes exactly 1 kWh.

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