Electric Power

In one sentence: Electric power tells you how fast a device uses energy, and you get it by multiplying the volts by the amps to get watts.

$P = V I$

Read it out loud: “P equals V times I. Power in watts equals volts times amps.”

What each symbol means

Symbol	Meaning
$P$	Power, how fast electrical energy is used or delivered, measured in watts (W). One watt is one joule of energy per second.
$V$	Voltage, the electrical push across the device, measured in volts (V).
$I$	Current, the flow of charge through the device, measured in amperes (A).

What the formula is doing

Power is a rate: it says how much energy a device uses or delivers each second. Its unit is the watt (W), named after James Watt. A device rated at 2000 W uses 2000 joules of energy every second while it runs.

The formula $P = V I$ says power is the voltage times the current. Voltage $V$ is the push, in volts (V). Current $I$ is the flow, in amperes (A). A bigger push or a bigger flow gives more power, and multiplying the two gives watts.

Ohm’s law lets you rewrite the same formula with resistance $R$ in ohms ( $\Omega$ ). Since $V = I R$ , you get $P = I^2 R$ when you know the current, and $P = \frac{V^2}{R}$ when you know the voltage. All three versions give the same answer for a resistor, so use whichever pair of numbers you already have.

Mains voltage is dangerous. It is 230 V in much of the world and 120 V in North America, and it can cause a lethal shock. Do not open mains devices such as kettles, heaters or chargers to test them, and get a qualified person to repair them.

An everyday picture

Think of a water wheel. The voltage is how high the water falls, the current is how much water flows past each second, and the power is how hard the wheel turns. A tall fall with a big flow turns the wheel hard. A tall fall with a trickle, or a big flow over a short drop, does much less.

Worked example: A 2000 W kettle on 230 V and on 120 V

A kettle is rated at $P = 2000\ \text{W}$ . Mains supplies vary by region: first the kettle runs on a 230 V supply, then the same 2000 W is needed from a 120 V supply. How much current does it draw in each case? Do not open the kettle to check; the wiring is at mains voltage.

Rearrange $P = V I$ to get the current: $I = \frac{P}{V}$ .
On 230 V: $I = \frac{2000\ \text{W}}{230\ \text{V}} \approx 8.70\ \text{A}$ .
On 120 V: $I = \frac{2000\ \text{W}}{120\ \text{V}} \approx 16.7\ \text{A}$ .
Check the 230 V case: $8.70\ \text{A} \times 230\ \text{V} = 2001\ \text{W}$ , which is 2000 W with rounding.

Answer: The kettle draws about 8.70 A on 230 V. The same 2000 W on 120 V draws about 16.7 A, nearly twice the current, so the wiring has to carry much more current for the same power.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Mixing up watts and watt-hours. A watt is a rate, while a watt-hour is an amount of energy. The page on energy and kilowatt-hours explains the difference.
Forgetting to convert units. 20 mA is 0.02 A, not 20 A, so convert milliamps to amps before you multiply.
Assuming the power stays the same when the voltage changes. For a fixed resistance, power grows with the square of the voltage, $P = V^2 / R$ , so a small change in voltage makes a big difference.
Opening a mains device to measure its power. The voltage can cause a lethal shock, and the wiring stays dangerous even when the device is switched off.

Where you will meet it

Appliance labels and electricity bills, where each device is rated in watts.
Choosing a fuse, circuit breaker or power supply that can carry the current a device will draw.
Rating solar panels, batteries and chargers, which list their output power in watts.
Heaters and electric motors, where the power rating shows how much heat or work the device can deliver.

Questions people ask

What is the difference between a volt and a watt?

A volt measures the push (voltage). A watt measures the rate of energy use (power). A device can have a high voltage and still use little power if very little current flows.

Can I use P = V I for a battery?

Yes. For a battery, $V$ is the voltage it delivers and $I$ is the current it supplies, so $P$ is the power it hands to the device.

How many watts are in a kilowatt?

One kilowatt (kW) is 1000 W. A 2 kW heater uses 2000 W while it runs.

Are $P = V I$ and $P = I^2 R$ different formulas?

They are the same formula for a resistor, because Ohm’s law links $V$ and $I$ through $R$ . Pick whichever pair of numbers you have.

Ohm's Law: Ohm’s law says the push on a wire, the voltage, equals the flow through it, the current, times how hard that flow is to get through, the resistance.
Energy and Kilowatt-Hours: Energy is power multiplied by time, so a heater that uses 2 kilowatts for 3 hours uses 6 kilowatt-hours of energy.
Resistors in Series and Parallel: Resistors in a line add up, and resistors side by side always give a total smaller than the smallest one.