Energy Converter

How the energy units are defined

The joule is the SI unit of energy: the work done by a force of one newton over one meter, or one watt flowing for one second. Every other unit in this converter is a fixed number of joules, and all of those numbers are exact by definition.

• Watt-hours. One watt for one hour is 3,600 J, so a kilowatt-hour is exactly 3.6 MJ. This is the unit on an electricity bill.
• Calories. The calorie began as the heat that warms a gram of water by 1 °C, but that amount depends on the water’s starting temperature, so it was replaced by fixed definitions. The thermochemical calorie is exactly 4.184 J; the International Table calorie, adopted in 1956 for steam tables, is exactly 4.1868 J. A kilocalorie is 1,000 of either.
• Btu and therm. The International Table Btu is defined through its value per pound, exactly 2.326 kJ/kg, which makes one Btu exactly 1,055.05585262 J. The US therm is legally 105,480,400 J, which is 100,000 of an older “59 °F” Btu and about 99,976 of the IT Btu used here.
• Mechanical and physics units. A foot-pound is one pound-force acting over one foot: 0.3048 m × 4.4482216152605 N = 1.3558179483314004 J. The electronvolt is the energy an electron gains across one volt, exactly 1.602176634 × 10⁻¹⁹ J since the elementary charge was fixed in 2019. The erg, from the older CGS system, is 10⁻⁷ J.

The conversion formula

Because every unit is a whole number of joules or an exact fraction of one, a conversion is one multiplication:

value

the amount of energy you enter

joules in a unit

e.g. 3,600,000 for the kilowatt-hour, 4,184 for the kilocalorie, 1,055.05585262 for the Btu

The definitions used, in joules:

Worked examples

1 kWh to Btu. 3,600,000 J ÷ 1,055.05585262 J = 3,412.141633 Btu. The figure of 3,412 Btu per kWh that utilities and the US Energy Information Administration quote is this value, rounded.

A 100 kcal snack in kilojoules. 100 × 4.184 = 418.4 kJ, exactly.

One therm of natural gas. 105,480,400 J is 105.4804 MJ, or 29.30011111 kWh, and 99,976.12898 Btu (IT). To compare a gas bill with an electricity bill, this is the number that matters.

An electronvolt in joules. 1 eV = 1.602176634 × 10⁻¹⁹ J, a tiny amount: a kilowatt-hour is about 2.246943267 × 10²⁵ eV.

Which calorie is on a food label?

The “Calorie” on a nutrition label, often written with a capital C, is the kilocalorie: 1,000 small calories. A snack labelled 100 Calories contains 100 kcal, about 418 kJ.

Sources don’t agree on which kilocalorie that is. The FAO’s report on food energy converts with 1 kcal = 4.184 kJ, the thermochemical value, and this converter uses it. NIST’s guide to the SI lists the nutrition kilocalorie as the International Table one, 4.1868 kJ. The two differ by less than 0.07%, far smaller than the uncertainty in the energy content of any real food, so it does not matter for eating; it matters only if you need to reproduce a published figure digit for digit. The IT calorie is also in the list if you need it.

Energy content of common fuels

The US Energy Information Administration publishes sample heat contents for fuels in Btu. Converted with the IT Btu, they are:

These are averages; the real figure varies with the fuel blend and season. They are the chemical energy in the fuel, not the work you get out of it: an engine or furnace turns only part of it into motion or useful heat. To turn kilowatt-hours into money, use the electricity cost calculator.

Mistakes to avoid

• Mixing up energy and power. A watt is a rate (joules per second); a watt-hour is an amount of energy. A 2 kW heater running for 3 hours uses 6 kWh.
• Mixing up calories and Calories. A food Calorie is 1,000 calories. A “250 calorie” snack means 250 kcal, not 250 cal.
• Assuming a therm is exactly 100,000 Btu. It is, in the older 59 °F Btu, but in the IT Btu used for most modern figures it is 99,976 Btu. The 0.024% gap rarely matters, but it explains small mismatches between tables.
• Confusing the foot-pound of energy with the pound-foot of torque. They have the same dimensions, but torque is not energy. Convert torque separately.