Units of energy and their equivalents
| Unit | Symbol | In joules |
|---|---|---|
| Kilowatt-hour | kWh | 3,600,000 J |
| Joule | J | 1 Jbase unit |
| Kilojoule | kJ | 1,000 J |
| Kilocalorie | kcal | 4,184 J |
| Calorie | cal | 4.184 J |
| Watt-hour | Wh | 3,600 J |
| Megajoule | MJ | 1,000,000 J |
| British thermal unit | BTU | 1,055 J |
Frequently asked questions
Is the kilowatt-hour a unit of power?
No, it is energy. The kilowatt is a power, that is a rate; the kilowatt-hour is what that rate delivers over one hour. A 2 kW heater on for three hours uses 6 kWh, and that is the quantity the bill counts. One kilowatt-hour is exactly 3,600,000 joules, or 3.6 megajoules, since an hour holds 3600 seconds.
Why does a label show both calories and kilocalories?
Because the nutritional Calorie, capitalised in American usage, is really a kilocalorie, a thousand physical calories. A yoghurt marked 100 Calories therefore holds 100 kcal, that is one hundred thousand calories in the physicist's sense. European regulation 1169/2011 requires both figures, kilojoules then kilocalories, which removes the ambiguity: 100 kcal is also 418 kJ.
How many joules in a BTU?
One BTU is 1055.05585262 joules in its international definition, the one air conditioning tables use. It is the energy that raises one pound of water by one degree Fahrenheit. It is met mostly as a power: a 12,000 BTU per hour air conditioner delivers 3.517 kilowatts, and the same machine is sold under one label or the other depending on the continent.
Kilowatt-hour or kilowatt-peak on a solar quote?
The kilowatt-peak measures a power, not an output. It is what a panel delivers under standardised test conditions, a thousand watts per square metre at twenty-five degrees, that is a laboratory full sun. The kilowatt-hour measures what the installation actually produces over a year. At mid latitudes one kilowatt-peak returns between 1000 and 1300 kilowatt-hours a year depending on region and orientation, so a 3 kWp array produces roughly 3000 to 3900 kWh.
What is a therm on a gas bill?
An English-language unit worth one hundred thousand BTU, that is 105.5 megajoules or 29.3 kilowatt-hours. The United Kingdom and the United States bill gas in therms where continental Europe bills it in kilowatt-hours, which makes price comparisons misleading until both are brought to the same unit. Energy for energy, one therm costs what twenty-nine and a third kilowatt-hours cost.
Heat and work are the same thing
James Joule established it around 1845 by turning a paddle wheel inside a barrel of water, driven by a falling weight. The water warmed in exact proportion to the work supplied, and heat stopped being a separate substance to become a form of energy. That is why one unit is enough to measure a meal, an electricity bill and the stroke of a piston, and why moving between them is a plain factor.
The orders of magnitude still mislead. A joule is tiny: roughly the energy needed to lift an apple by one metre. A kilowatt-hour is 3.6 million of them and runs a fridge for a day. A 2000 kilocalorie diet is 8.4 megajoules, that is 2.3 kilowatt-hours, less than one tumble dryer cycle. In energy terms, a human body consumes about as much as a large household appliance.