Energy Conversion Calculator — J, kWh, Btu and Calories

Background.

One household can meet the same physical quantity in four different costumes in a single week. The electricity bill counts kilowatt-hours. An American gas bill counts therms of 100,000 Btu. The cereal box gives kilocalories, and in Europe kilojoules beside them. A physics worksheet wants joules. Comparing any two of them means passing through a common unit, and the joule is the unit every definition here is tied to.

Type an amount, say what unit it is in and which unit you want, and you get the converted figure plus the same energy expressed in all nine supported units: joules, kilojoules, megajoules, watt-hours, kilowatt-hours, thermochemical calories and kilocalories, International Table British thermal units, and foot-pounds-force. Seeing them side by side is a useful check in itself. A slip by a factor of 1,000, such as calories for kilocalories or watt-hours for kilowatt-hours, is the mistake people make most often with energy units, and it is obvious when 860 sits next to 860,421.

Several of these relationships are exact. A watt is a joule per second and an hour is 3,600 seconds, so a kilowatt-hour is precisely 3.6 megajoules. Others carry a hidden choice. The word calorie can mean the thermochemical calorie of exactly 4.184 J used here, the International Table calorie of 4.1868 J found in steam tables, or, written with a capital C on food packaging, a whole kilocalorie. The Btu has several historical versions too; the one offered is the International Table Btu, the usual choice in modern engineering.

A conversion says how much energy there is, not how much of it ends up doing what you want. A kilowatt-hour fed to an electric bar heater becomes about a kilowatt-hour of heat in the room, while the same 3.6 MJ of petrol burned in a car engine leaves most of it as waste heat. Efficiency, price and time sit outside this arithmetic.

What is energy conversion calculator?

Energy is the capacity to do work or transfer heat, and a unit of energy is just an agreed-upon amount of it. The SI unit is the joule: the work done when a force of one newton pushes something one metre, which is also one watt sustained for one second. The other units grew up in particular trades. Watt-hours and kilowatt-hours come from electricity metering, where power multiplied by time is the natural measure. Calories and British thermal units began as heat units defined by warming water — a gram by one degree Celsius, a pound by one degree Fahrenheit — and have since been redefined as fixed numbers of joules. The foot-pound-force is the work done by a one-pound force acting over one foot. Converting between them changes the number, never the energy. For a sense of scale, lifting a 102 g apple through one metre takes about one joule, while a single kilowatt-hour would be enough to raise a tonne roughly 367 metres — which is why everyday electricity use is counted in kilowatt-hours rather than in joules.

How to use this calculator.

1. 01Type the amount in the Energy field. Decimals are fine, and negative values are kept as negative when the sign means energy leaving a system; the field accepts magnitudes up to one trillion.
2. 02Set From unit to match your source exactly. A food label's Calories are kilocalories, so choose kcal; an electricity bill or an EV charger's display is in kWh; Btu figures from American heating, cooling and gas paperwork belong under Btu (IT).
3. 03Set To unit to the unit you need. The full breakdown below the main answer lists the same energy in every unit, so you can read several conversions without changing the menu.
4. 04Use the megajoule or joule line as a sanity check on scale before copying a number into a report or a spreadsheet.
5. 05If your figure is a rate — kilowatts, horsepower or Btu per hour — it is power, not energy. Multiply it by the running time in hours first, then convert the energy.

The formula.

Every conversion goes through the joule. The amount you enter is multiplied by the number of joules in its unit, and that total is divided by the number of joules in the target unit: converted = value × J(from) ÷ J(to). The same joule total feeds every line of the breakdown, so all nine figures agree with one another. The factors are J = 1, kJ = 1,000, MJ = 1,000,000, Wh = 3,600 and kWh = 3,600,000, all exact from the SI prefixes and the 3,600 seconds in an hour. The thermochemical calorie is defined as exactly 4.184 J, so its kilocalorie is 4,184 J. The International Table Btu is 1,055.05585262 J, and that awkward number has a tidy origin: it is the International Table calorie of 4.1868 J per gram per degree Celsius, multiplied by the 453.59237 grams in a pound and by 5/9 to turn a Celsius degree into a Fahrenheit one. Because the Btu rests on the slightly larger IT calorie, one Btu is 252.1644 thermochemical calories rather than a round 252. The foot-pound-force is 0.3048 m × 0.45359237 kg × 9.80665 m/s², the international foot times the pound's mass times standard gravity, which gives 1.3558179483314004 J; one Btu is therefore about 778.1693 ft·lbf. Results are carried to ten decimal places of the target unit and shown to four, switching to scientific notation below 0.001. No physical assumption enters the calculation, so the only way to get a wrong answer is to start from the wrong unit: the calorie-versus-kilocalorie and watt-hour-versus-kilowatt-hour mix-ups give answers off by exactly 1,000, while choosing a different calorie or Btu definition from your source shifts results by less than a tenth of a percent.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B.8 supplies energy/work conversion factors including Btu (IT), thermochemical calorie, watt-hour and foot-pound-force.
2. [2]BIPM SI Brochure defines joule, watt and the SI prefix system.
3. [3]NIST SP 330 independently lists joule and watt in the SI derived-unit table.
4. [4]FDA Nutrition Facts guidance supplies the scope for capital-C dietary Calories.
5. [5]NIST Handbook 44 Appendix C provides a customary/SI legal-metrology cross-check.