Energy, power and the kilowatt-hour

Welcome to the island. Its people need electricity for lights, fridges, phones, pumps and heaters. Before you can supply it, you have to count it, and counting needs two ideas that people often mix up.

• Energy is the amount of work that can be done. Its SI unit is the joule (J).
• Power is how fast energy is used or delivered. Its unit is the watt (W), and 1 W = 1 J per second.

The link is P = E / t, or E = P × t. Energy is like the water in a tank. Power is like the speed the water runs out of the tap.

A joule is tiny, so electricity bills use a bigger unit, the kilowatt-hour (kWh). It is the energy used by a 1 kW device running for 1 hour.

• 1 kW = 1,000 W, so 1 kWh = 1,000 W × 3,600 s = 3,600,000 J = 3.6 MJ.
• A 10 W LED bulb running for 100 hours uses 10 W × 100 h = 1,000 Wh = 1 kWh.
• A 2 kW heater running for 3 hours uses 2 kW × 3 h = 6 kWh.
• A 3 kW kettle running for 3 minutes (0.05 h) uses 3 kW × 0.05 h = 0.15 kWh.

The prefix ladder. Each step is a factor of 1,000.

• kW (kilowatt): 10³ W. A hot-water kettle, a hair dryer, one home's peak demand.
• MW (megawatt): 10⁶ W. One large wind turbine, a small town.
• GW (gigawatt): 10⁹ W. A large power station, a big city.
• TWh (terawatt-hour): 10¹² Wh. A country's electricity use is counted in TWh per year.

Check the habit of reading units. MW is a rate. MWh is an amount. A 3 MW turbine running for 2 hours delivers 6 MWh.

How much does a home use? It varies a lot with the country, the climate and whether heating or cooling runs on electricity. As a rough guide, a typical home uses somewhere between 5 and 30 kWh per day: lower in many mild-climate European homes, higher in places with electric heating or air conditioning, such as the average US home. Your island's example home will use about 10 kWh a day. It is an assumed number for this lab.

For scale, a phone battery holds about 15 Wh (0.015 kWh). A full charge costs very little energy, which is why a phone charger is a tiny part of a home's total.