Science
What is electrical power, and how do you calculate it?
Quick answer
Electrical power is how fast electricity transfers energy. P = V × I (watts = volts × amps), so a 230 V kettle drawing 10 A has a power of 2,300 W.
In one sentence
Electrical power tells you how quickly an electrical device uses energy, and you find it by multiplying the voltage by the current.
Explained
A kettle and a phone charger both plug into the wall, but the kettle can boil water in a few minutes while the charger barely gets warm. The difference is power: how many joules of energy a device transfers every second. Power is measured in watts (W), and 1 watt = 1 joule per second. Big powers are given in kilowatts: 1 kW = 1,000 W.
For anything electrical, the power depends on two things: the voltage (the push that drives the current, in volts) and the current (how much charge flows each second, in amps). The formula is:
P = V × I (power in watts = voltage in volts × current in amps)
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Why does it work? Voltage tells you how many joules each coulomb of charge carries (1 V = 1 J/C). Current tells you how many coulombs pass every second (1 A = 1 C/s). Multiply them and the coulombs cancel: joules per second, which is watts. A 230 V supply giving 10 A transfers 230 × 10 = 2,300 J every second, so the power is 2,300 W (2.3 kW).
The water analogy helps. Think of a hose: the voltage is like the water pressure, the current is like how much water flows per second, and the power is how much work the water can do each second, for example how fast it could turn a water wheel. More pressure or more flow means more power.
You can rearrange P = V × I with a formula triangle (P on top, V and I underneath): I = P ÷ V and V = P ÷ I. Combining it with Ohm's law (V = I × R) gives two more versions, which are useful when you know the resistance R in ohms:
- P = I² × R: power from current and resistance (the heating effect of a current)
- P = V² ÷ R: power from voltage and resistance
Power is not the same as energy. Power is the rate; energy is the total. To find the energy, multiply by the time:
E = P × t (joules = watts × seconds)
Electricity companies use a bigger unit, the kilowatt-hour (kWh): the energy used by a 1 kW device in 1 hour. 1 kWh = 1,000 W × 3,600 s = 3,600,000 J (3.6 MJ). The bill is the number of kWh × the price of one kWh. This connects to the wider topic of energy and to how circuits work.
Mains voltage is about 230 V in the UK, Europe, Nigeria, India and much of the world, and about 120 V in the US and Canada (see electricity). So the same 1,500 W hair dryer draws about 6.5 A in London but 12.5 A in New York.
Examples
| Device | Voltage | Current | Power (P = V × I) |
|---|---|---|---|
| Torch bulb | 3 V | 0.5 A | 1.5 W |
| Phone charging over USB | 5 V | 2 A | 10 W |
| Laptop charger | 20 V | 3 A | 60 W |
| Kettle on a 230 V supply | 230 V | 10 A | 2,300 W (2.3 kW) |
| Hair dryer on a 120 V supply | 120 V | 12.5 A | 1,500 W (1.5 kW) |
| Car starter motor | 12 V | 150 A | 1,800 W (1.8 kW) |
Worked example: a 2 kW electric heater is on for 3 hours. Energy = 2 kW × 3 h = 6 kWh. If electricity costs 25 cents per kWh, that costs 6 × 25 = 150 cents ($1.50). In joules: 2,000 W × 10,800 s = 21,600,000 J.
Common mistakes
- Mixing up power and energy. kW is power (how fast); kWh is energy (how much). A kettle has a high power but is on for only a few minutes.
- Forgetting to convert the time. For joules, use seconds (2 minutes = 120 s). For kWh, use hours (30 minutes = 0.5 h) and kilowatts.
- Rearranging the wrong way. I = P ÷ V, not V ÷ P. Check with the triangle: cover I and you see P over V.
- Mixing W and kW, or mA and A. 2,000 W = 2 kW; 500 mA = 0.5 A. Convert before you calculate.
- Thinking volt-amps are always watts. For batteries and heaters they match, but for some AC devices with motors, the VA figure is bigger than the real power in watts.
Step by step
Step by step
- List what you knowWrite down the values you are given: power P, voltage V, current I, resistance R or time t.
- Pick the formulaV and I: P = V × I. I and R: P = I² × R. V and R: P = V² ÷ R. Energy: E = P × t.
- Convert the unitsWatts, volts, amps and ohms; seconds for joules, or kW and hours for kWh.
- Substitute and calculatePut the numbers in and work it out. Rearrange first if the unknown is not P.
- Write the unitW or kW for power; J or kWh for energy. Check the size makes sense.
Practice questions
Electrical power calculations
Try each one, then check your answer.
- A lamp runs on 6 V with a current of 2 A. What is its power?
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P = 6 × 2 = 12 W - A device on a 230 V supply draws 4 A. Find its power.
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P = 230 × 4 = 920 W - A lamp on a 120 V supply draws 0.5 A. Find its power.
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P = 120 × 0.5 = 60 W - What current does a 60 W bulb draw from a 230 V supply?
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I = P ÷ V = 60 ÷ 230 ≈ 0.26 A - What current does a 2,300 W kettle draw from a 230 V supply?
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I = 2,300 ÷ 230 = 10 A - A 24 W device draws 2 A. What voltage does it run on?
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V = P ÷ I = 24 ÷ 2 = 12 V - How much energy does a 40 W lamp transfer in 60 seconds?
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E = 40 × 60 = 2,400 J - A 1,000 W microwave runs for 2 minutes. How much energy does it transfer?
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E = 1,000 × 120 = 120,000 J (120 kJ) - A kettle transfers 180,000 J in 90 s. What is its power?
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P = E ÷ t = 180,000 ÷ 90 = 2,000 W (2 kW) - Write 2,500 W in kilowatts.
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2,500 ÷ 1,000 = 2.5 kW - A 3 kW heater is on for 4 hours. How many kWh does it use?
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3 × 4 = 12 kWh - A 100 W TV is on for 5 hours. How many kWh is that?
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0.1 kW × 5 h = 0.5 kWh - A current of 2 A flows through a 6 Ω resistor. Find the power.
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P = I² × R = 2² × 6 = 24 W - A 4 Ω resistor is connected to 12 V. Find the power.
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P = V² ÷ R = 12² ÷ 4 = 144 ÷ 4 = 36 W - How many joules are there in 1 kWh?
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1,000 W × 3,600 s = 3,600,000 J (3.6 MJ)
Word problems
Power at home
Try each one, then check your answer.
- A phone charger gives 5 V and 2 A for 2 hours. Find its power and the energy it transfers.
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P = 5 × 2 = 10 W; E = 10 × 7,200 = 72,000 J (0.02 kWh) - A 2 kW heater is on for 3 hours a day for 7 days. Electricity costs 25 cents per kWh. What does it cost?
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2 × 3 × 7 = 42 kWh; 42 × 0.25 = $10.50 - A 60 W old-style bulb is replaced by an 8 W LED bulb. Both are on for 5 hours a day for 30 days. How much energy is saved?
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(60 − 8) × 5 × 30 = 7,800 Wh = 7.8 kWh - A 2,000 W kettle takes 3 minutes to boil. How much energy does it transfer?
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2,000 × 180 = 360,000 J (0.1 kWh) - A 1,800 W hair dryer is used on a 120 V supply in the US and on a 230 V supply in Europe. What current does it draw in each place?
Show answer
1,800 ÷ 120 = 15 A in the US; 1,800 ÷ 230 ≈ 7.8 A in Europe
Questions people ask
What is the formula for electrical power?
P = V × I: power in watts equals voltage in volts times current in amps. Other forms are P = I² × R, P = V² ÷ R and P = E ÷ t (energy divided by time).
What is the unit of electrical power?
The watt (W), named after James Watt. 1 W is 1 joule per second. Larger powers use kilowatts (1 kW = 1,000 W) and megawatts (1 MW = 1,000,000 W).
What is the commercial unit of electrical energy?
The kilowatt-hour (kWh), often just called a "unit" on electricity bills. It is the energy a 1 kW appliance uses in 1 hour, and it equals 3.6 × 10⁶ joules.
What is the difference between watts, volts and amps?
Volts measure the push (potential difference), amps measure the flow of charge (current), and watts measure how fast energy is transferred (power). Watts = volts × amps. With resistance in ohms, Ohm's law V = I × R links them all.
How do you get amps from watts and volts?
Divide the power by the voltage: I = P ÷ V. A 1,150 W toaster on a 230 V supply draws 1,150 ÷ 230 = 5 A.
Are volt-amps the same as watts?
For a battery circuit or a heater, yes. For some AC devices with motors or power supplies, the current and voltage are slightly out of step, so the real power in watts is less than volts × amps. That bigger figure is called the apparent power, in volt-amps (VA). The ratio between them is the power factor.
What is more dangerous: volts, amps or watts?
It is the current flowing through a body that causes harm, and it takes a high enough voltage to push a dangerous current through you. The watts on a label tell you how much energy an appliance uses, not how dangerous it is. Treat every mains socket as dangerous.
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Electricity is the flow of tiny charged particles called electrons through a material. It powers lights, phones and machines, and it can come from batteries or the mains supply.
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An electric circuit is a complete loop that electricity flows around. A simple circuit has a battery, wires and a component like a bulb. If the loop is broken, the electricity stops.
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