Electrical power calculator: P = IV and P = I²R

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Choose the equation that matches the values you have, then enter two to find the third. Both come from GCSE and IGCSE physics:

P = I \times V \qquad\qquad P = I^2 \times R

where $P$ is power in watts (W), $I$ is current in amps (A), $V$ is potential difference in volts (V) and $R$ is resistance in ohms (Ω). Use $P = IV$ when you know the voltage, and $P = I^2R$ when you know the resistance.

Current (I)

Potential difference (V)

power

690 W

Show in

Working

1Equation: power = current × potential difference
2Substitute: power = 3 A × 230 V
3Power = 690 W

Electricity homework? The AI tutor explains power, current and resistance step by step.Try it free

Rearranging both equations

To find	From $P = IV$	From $P = I^2R$
Power	$P = I \times V$	$P = I^2 \times R$
Current	$I = \dfrac{P}{V}$	$I = \sqrt{\dfrac{P}{R}}$
Voltage / resistance	$V = \dfrac{P}{I}$	$R = \dfrac{P}{I^2}$

Worked examples

Kettle: a kettle on the 230 V mains draws 3 A. $P = 3 \times 230 = 690$ W.
Resistor: a current of 2 A flows through a 10 Ω resistor. $P = 2^2 \times 10 = 40$ W.
Current from power: a 40 W heater with resistance 10 Ω. $I = \sqrt{40 \div 10} = 2$ A.
Fuse choice: a 2,300 W hairdryer on 230 V draws $2300 \div 230 = 10$ A, so it needs a fuse rated a little above 10 A, such as 13 A.

Where P = I²R comes from

Combine $P = IV$ with Ohm's law, $V = IR$ : substituting gives $P = I \times IR = I^2R$ . It shows why power cables lose energy as heat: the loss depends on the current squared. The National Grid uses very high voltages so the current, and therefore the $I^2R$ loss, is small. For Ohm's law itself, use our Ohm's law calculator.

Energy from power

Energy transferred $= P \times t$ (power × time in seconds). A 690 W kettle on for 2 minutes transfers $690 \times 120 = 82800$ J. You can also use $E = QV$ : charge × potential difference. Our charge calculator finds $Q$ from current and time.

Common mistakes

Forgetting to square the current in $P = I^2R$ .
Using milliamps without converting: 500 mA is 0.5 A.
Using $P = IV$ with the voltage across a different component.

Practise with our electrical power questions.

Mains electricity facts

UK mains is about 230 V a.c. at 50 Hz.
Power ratings on appliances are in watts: a kettle is around 2,000 to 3,000 W, a laptop charger tens of watts.
The fuse rating should be just above the normal current: work out $I = P \div V$ , then pick the next fuse size up (common UK sizes are 3 A, 5 A and 13 A).
High-power appliances have earthed metal cases and thicker cables to carry the larger current safely.

Frequently asked questions

What is the formula for electrical power?

P = I × V (current × potential difference), or P = I² × R (current squared × resistance). Both give power in watts.

How do I find current from power and voltage?

Divide power by voltage: I = P ÷ V. A 1,150 W appliance on 230 V draws 5 A.

Why does the National Grid use high voltage?

For the same power, a higher voltage means a lower current, and power lost as heat in the cables depends on the current squared (P = I²R).

Is anything I type sent to a server?

No. The calculation runs in your browser and nothing is stored.

Sources

GCSE Physics (8463) specification: subject content. AQA.
Cambridge IGCSE Physics 0625 syllabus for 2026, 2027 and 2028. Cambridge International.

Electrical power questions and answers

8 GCSE and IGCSE questions with worked answers, checked as you type.

Ohm's law calculator: voltage, current or resistance

Voltage, current or resistance from the other two using V = IR, with units and working.

Ohm's law explained: V = IR, I–V graphs and components

V = IR with worked examples, I–V graphs for each component, and the resistance practical.

An AI physics tutor for forces, motion, energy and more

Choose the right equation, handle units and rearrange formulas: physics problems worked through one step at a time.