How to read this page
Energy turns up in many units: joules in physics, kilowatt-hours on an electricity bill, British thermal units (Btu) in fuel statistics, kilocalories on food labels and electronvolts in descriptions of light. They all measure the same physical quantity. This page sets them side by side with their size in joules, so that any of them can be turned into any other.
Every factor here comes from one of two places. The conversion factors to joules and watts are from Appendix B.8 of NIST's Guide to the SI, the US National Institute of Standards and Technology's reference table. Factors that the US Energy Information Administration (EIA) uses for comparing fuels are from its Energy Explained pages and are labelled as such. NIST writes its factors in scientific notation, for example 3.6 E+06 for 3.6 × 10⁶; they are written out in ordinary notation below.
Factors are given to the precision NIST prints, or rounded where the table says "about". Nothing on this page is a measurement of a real appliance, food or fuel.
Energy units
The SI unit of energy, work and amount of heat is the joule (J). NIST expresses it as one newton metre: the work done by a force of one newton acting through one metre.
| Unit | Symbol | In joules | Where it is used | Source |
|---|---|---|---|---|
| joule | J | 1 J | Physics and the SI generally | NIST SI Chapter 4 |
| electronvolt | eV | about 1.602 177 × 10⁻¹⁹ J | Energy of photons and particles | NIST Appendix B.8 |
| calorie (thermochemical) | calth | 4.184 J | Chemistry | NIST Appendix B.8 |
| calorie (International Table) | calIT | 4.1868 J | Heat measurement | NIST Appendix B.8 |
| kilocalorie (thermochemical) | kcalth | 4,184 J | Food energy ("calories" on labels) | NIST Appendix B.8 |
| kilocalorie (International Table) | kcalIT | 4,186.8 J | Food energy | NIST Appendix B.8 |
| British thermal unit (International Table) | BtuIT | about 1,055.056 J | US fuel and heating statistics | NIST Appendix B.8 |
| watt-hour | W·h | 3,600 J | Small amounts of electrical energy | NIST Appendix B.8 |
| kilowatt-hour | kW·h, kWh | 3,600,000 J (3.6 MJ) | Electricity bills and statistics | NIST Appendix B.8 |
| therm (US) | thm | about 105,480,400 J (about 105.5 MJ) | Natural gas | NIST Appendix B.8 |
The EIA uses its own rounded factors for comparing fuels, with the Btu as the common unit. The EIA defines a Btu as the amount of heat needed to raise the temperature of one pound of water by one degree Fahrenheit, and compares a single Btu to roughly the energy released by burning a match.
| Energy source | Physical unit | Btu |
|---|---|---|
| Electricity | 1 kilowatt-hour | 3,412 Btu |
| Natural gas | 1 cubic foot | 1,036 Btu |
| Natural gas | 1 therm | 100,000 Btu |
| Motor gasoline | 1 gallon | 120,214 Btu |
| Heating oil | 1 gallon | 138,500 Btu |
| Propane | 1 gallon | 91,452 Btu |
The two sets agree. NIST's factors give one kilowatt-hour as 3,600,000 ÷ 1,055.056, or about 3,412 Btu, which is the EIA's electricity factor. The EIA notes that its fuel factors are recalculated every year to reflect changes in fuel quality and composition, so the gasoline, gas and oil values above are samples rather than fixed constants.
Power units
Power is the rate of using or delivering energy. NIST defines the watt (W), the SI unit of power, as one joule per second.
| Unit | Symbol | In watts | Source |
|---|---|---|---|
| watt | W | 1 W = 1 J/s | NIST SI Chapter 4 |
| kilowatt | kW | 1,000 W | NIST SI Chapter 4 (prefix kilo) |
| horsepower (electric) | hp | 746 W | NIST Appendix B.8 |
| BtuIT per hour | Btu/h | about 0.293 071 W | NIST Appendix B.8 |
The most common confusion in household energy is between the kilowatt and the kilowatt-hour. The kilowatt is a unit of power, a rate. The kilowatt-hour is a unit of energy, an amount: one kilowatt sustained for one hour. The home energy guide works through the difference with examples.
SI prefixes
NIST's Guide to the SI lists the prefixes that form multiples of any SI unit. The ones that appear most often with energy and power are:
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| kilo | k | 10³ = 1,000 | kilojoule (kJ), kilowatt (kW) |
| mega | M | 10⁶ = 1,000,000 | megajoule (MJ), megawatt (MW) |
| giga | G | 10⁹ | gigawatt (GW) |
| tera | T | 10¹² | terajoule (TJ), terawatt-hour (TWh) |
| peta | P | 10¹⁵ | petajoule (PJ) |
The EIA uses a non-SI shorthand for very large amounts: a quad is one quadrillion Btu, that is 10¹⁵ Btu, a 1 followed by 15 zeros. National energy totals are usually counted in quads.
The SI itself rests on seven base units, NIST explains, among them the metre, the kilogram, the second, the ampere and the kelvin. The joule and the watt are derived units built from them: the joule is a kilogram metre squared per second squared, and the watt is a joule per second.
How to convert
Every conversion on this site follows the same two steps: turn the starting amount into joules, then turn the joules into the unit you want.
- Multiply the amount by its size in joules from the table.
- Divide the result by the size in joules of the target unit.
Worked example
Arithmetic only, with no real product or bill in mind. How many kilocalories are in 2 kilowatt-hours?
- Into joules: 2 × 3,600,000 = 7,200,000 J.
- Into thermochemical kilocalories: 7,200,000 ÷ 4,184, about 1,721 kcal.
And the other way: 500 kcal is 500 × 4,184 = 2,092,000 J, which is 2,092,000 ÷ 3,600,000, about 0.58 kWh.
A feel for the sizes
The table shows how far apart the units are. A kilowatt-hour is 3.6 million joules, and a kilocalorie is 4,184 joules, so one kilowatt-hour is about 860 kilocalories. A Btu, the EIA's match-flame of heat, is about a thousand joules. An electronvolt is so small that a single joule contains more than six billion billion of them.
Some useful relationships, each worked from the factors above:
- 1 kWh is about 860 kcal, about 3,412 Btu, and exactly 3.6 MJ.
- 1 kcal is about 4.2 kJ, about 4 Btu, and about 0.0012 kWh.
- 1 therm (US) is about 105.5 MJ, or about 29.3 kWh.
- 1 horsepower (electric) is 746 W, about three quarters of a kilowatt.
Three cautions
- There is more than one Btu and more than one calorie. NIST lists several versions of each, defined in slightly different ways. They differ by well under 1%, which does not matter for everyday arithmetic but does matter in precise science. This site uses the International Table Btu and the thermochemical calorie unless it says otherwise.
- Heat content is not delivered heat. The Btu content of a fuel says how much energy it holds, not how much reaches a room. Every heater converts its fuel with its own efficiency, as the conservation guide explains.
- Rounding builds up. Long chains of rounded conversions drift. When precision matters, convert once through joules using the full factors in the first table.
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