Power calculator: P = E ÷ t with working

Example: a motor transfers 1,200 J in 30 s. $P = 1200 \div 30 = 40$ W.

Convert to watts and seconds before using the equation.

Example: a 2 kW kettle is on for 3 minutes. $P = 2000$ W and $t = 180$ s, so $E = 2000 \times 180 = 360000$ J (360 kJ).

Electricity bills use a different energy unit, the kilowatt-hour (kWh): the energy a 1 kW appliance uses in one hour, which is $1000 \times 3600 = 3.6$ million joules.

For electrical appliances you can also use $P = I \times V$ (current × potential difference) or $P = I^2 \times R$. Our electrical power calculator does both. A 230 V appliance drawing 3 A has a power of 690 W.

A more powerful device transfers the same energy in less time. Two students climbing the same stairs do the same work against gravity, but the one who climbs faster has the higher power. If you know the work done, our work done calculator gives it from force and distance, and you can then divide by the time here.

• Using minutes instead of seconds.
• Confusing power (W) with energy (J).
• Forgetting to convert kW to W (× 1,000).

Practise with our power questions and the efficiency calculator.

• Always convert to watts and seconds first; leave the answer in the unit the question asks for.
• If the question is about lifting, find the work done ($W = mgh$ or $W = Fs$) first, then divide by the time.
• Compare answers with familiar values: a phone charger is about 5 to 20 W, a kettle about 2,000 to 3,000 W.
• If two people do the same work, the one who takes less time has more power: say so in words, not just numbers.

Example: a student of weight 500 N climbs stairs 4 m high in 5 s. Work done $= 500 \times 4 = 2000$ J, so power $= 2000 \div 5 = 400$ W.