Electricity companies measure energy in kilowatt-hours (kWh) rather than joules, because joules are too small for domestic use. One kWh equals 3.6 million joules — the energy needed to run a 1 kW appliance for one hour. At GCSE you must calculate energy transferred, convert units, and work out the cost of electricity.

What is electrical power and how does it relate to energy?

Power is the rate at which energy is transferred (or the rate at which work is done). For electrical appliances:

P = E / t

Rearranged: E = P × t

Symbol Quantity Standard unit
E Energy transferred Joule (J)
P Power Watt (W)
t Time Second (s)

1 watt = 1 joule per second

So a 60 W light bulb transfers 60 J of energy every second.

What is a kilowatt-hour?

A kilowatt-hour (kWh) is the amount of energy transferred by a 1 kW appliance running for 1 hour.

  • 1 kW = 1,000 W
  • 1 hour = 3,600 s

Therefore: 1 kWh = 1,000 W × 3,600 s = 3,600,000 J = 3.6 × 10⁶ J = 3.6 MJ

The kilowatt-hour is used for billing because it gives conveniently sized numbers. A typical UK household uses about 3,000–4,000 kWh of electricity per year.

How do you calculate energy in kilowatt-hours?

E (kWh) = P (kW) × t (hours)

Make sure to convert:

  • Power to kilowatts (divide watts by 1,000)
  • Time to hours (divide minutes by 60)

Worked example 1 — Electric kettle:

A kettle is rated at 2,500 W (2.5 kW). It is used for 4 minutes (4/60 = 0.0667 hours).

E = 2.5 × 0.0667 = 0.167 kWh

In joules: 0.167 × 3,600,000 = 600,000 J (0.6 MJ)

Worked example 2 — Television:

A television uses 120 W (0.12 kW) and is watched for 3 hours.

E = 0.12 × 3 = 0.36 kWh

In joules: 0.36 × 3,600,000 = 1,296,000 J

How do you calculate the cost of electricity?

Once you know the energy in kWh, multiply by the unit price:

Cost = E (kWh) × price per kWh (pence or £)

In the UK, the unit rate for electricity is set by the energy regulator and varies, but for exam calculations a typical value of 25–30 p per kWh (as of 2025–26) is used. Always use the value given in the question.

Worked example 3 — Annual cost of a fridge:

A fridge-freezer uses 400 W on average and runs continuously (8,760 hours per year).

E = 0.4 kW × 8,760 h = 3,504 kWh

Cost = 3,504 × £0.28 = £981 per year

(Note: modern fridge-freezers use far less — 150–250 kWh per year in practice — because they cycle on and off; this example uses a constant 400 W for simplicity.)

Comparing appliances by energy use

Appliance Typical power Used for Energy used
LED lamp 9 W (0.009 kW) 5 h/day 0.045 kWh/day
Laptop 50 W (0.05 kW) 4 h/day 0.2 kWh/day
Electric shower 9,000 W (9 kW) 8 min (0.133 h) 1.2 kWh per shower
Electric oven 2,000 W (2 kW) 1 h 2 kWh per use
Immersion heater 3,000 W (3 kW) 2 h 6 kWh per use

This table shows why showers and ovens dominate household electricity bills: they have high power ratings and are used frequently.

How do you convert between kWh and joules?

The conversion factor is 1 kWh = 3.6 × 10⁶ J (3.6 MJ).

To convert kWh → J: multiply by 3,600,000 (or 3.6 × 10⁶)

  • Example: 5 kWh = 5 × 3,600,000 = 18,000,000 J = 1.8 × 10⁷ J

To convert J → kWh: divide by 3,600,000

  • Example: 7,200,000 J = 7,200,000 / 3,600,000 = 2 kWh

In exams, always check which unit of energy the question asks for — both joules and kilowatt-hours appear on GCSE papers.

Frequently asked questions

Why do electricity companies use kWh instead of joules on bills?

A single joule is a very small amount of energy — one joule heats 0.24 g of water by 1 °C. Household energy consumption runs into billions of joules per year, making the joule awkward for billing. The kilowatt-hour gives numbers in the thousands rather than billions, which are easier to read, compare, and dispute. The same principle applies in food energy (kilojoules or kilocalories rather than joules) and in transport (megajoules per litre of fuel rather than joules).

How does a smart meter measure energy in kWh?

A smart meter measures the current drawn from the mains and the voltage of the supply, calculates power (P = V × I), and integrates power over time to accumulate energy in kilowatt-hours. It transmits readings remotely to the energy supplier, avoiding the need for estimated bills. Smart meters also allow time-of-use tariffs, where electricity is cheaper off-peak (e.g. overnight), incentivising use of appliances like dishwashers and washing machines during low-demand periods.

What is the relationship between watts, kilowatts, and megawatts?

These are all units of power, differing by factors of 1,000:

  • 1 kilowatt (kW) = 1,000 watts (W)
  • 1 megawatt (MW) = 1,000 kW = 1,000,000 W

A kettle is ~2.5 kW; a wind turbine generates ~2–3 MW; a large power station generates about 1,000–3,000 MW (1–3 GW). The National Grid transfers hundreds of GW at peak demand across the UK.

Most UK electricity still comes partly from gas-fired power stations. When global gas prices rise, electricity prices rise with them, because gas is burned to generate electricity. The UK's electricity price tripled between 2021 and 2023 primarily because of rising natural gas costs linked to supply disruptions. Renewable sources (wind, solar) have no fuel cost once built, so a higher proportion of renewables on the grid tends to reduce price volatility over the long term, even if capital costs for building them are high.

For Socratic GCSE physics with Professor Newton — predict the bill before you calculate it, then verify every figure — visit aitutors.me.