Energy Converter
Joules, calories, kilowatt-hours, BTU, therms and electronvolts — eleven units across 27 orders of magnitude, on exact defined factors. It also says out loud which calorie and which BTU it means, because there is more than one of each.
Convert an energy
The quantity you have, in the unit chosen below. Negative values are allowed — an enthalpy change has a sign.
The unit the quantity is already in. “cal” is the small calorie; a food label’s Calorie is “kcal”.
The unit you want the answer in. Every other unit is listed underneath the result anyway.
Everything routes through the joule: 1 kWh is 3,600,000 J, and one kJ is exactly 1,000 J.
- Conversion factor
- 1 kWh = 3,600 kJ
- Reverse factor
- 1 kJ = 0.0002777777778 kWh
- In joules
- 3,600,000 J
- Calories, both kinds
- 860,420.6501 small calories (cal) = 860.4206501 food Calories (kcal). The capital-C Calorie on a label is a thousand of the lower-case kind.
- Definition
- One kilojoule is exactly 1,000 joules.
| Unit | Symbol | Value |
|---|---|---|
| Electronvolts | eV | 2.246943267E25 |
| Joules | J | 3,600,000 |
| Foot-pounds | ft·lbf | 2,655,223.737 |
| Calories (small, cal) | cal | 860,420.6501 |
| Kilojoules | kJ | 3,600 |
| British thermal units | BTU | 3,412.141633 |
| Watt-hours | Wh | 1,000 |
| Kilocalories (food Calories) | kcal | 860.4206501 |
| Megajoules | MJ | 3.6 |
| Kilowatt-hours | kWh | 1 |
| Therms | therm | 0.03412141633 |
A food Calorie is a thousand calories — capital C, small c
This is the most common energy-unit mistake in the world, and it is not really the public’s fault. Two units share a name.
- The calorie (small c, “cal”) is 4.184 joules — roughly the heat that raises one gram of water by one degree Celsius. It is what a physicist, a chemist or a thermodynamics textbook means.
- The Calorie (capital C, “Cal”, properly “kcal”) is 1,000 of those — 4,184 joules. It is what every nutrition label, diet plan and fitness tracker means, even when it prints a lower-case “cal” next to the number.
So a chocolate bar at “250 calories” holds 250,000 calories in the physics sense, or 1,046,000 joules. A 2,000 Calorie day is 8.368 megajoules — about 2.32 kilowatt-hours, in the same range as a domestic fridge’s daily draw. Labels outside the United States print the kilojoule figure alongside, which is why an Australian muesli bar says 900 kJ and an American one says 215 Cal for the same food.
The distinction only bites in one direction. Nobody accidentally eats a thousand times too little; people convert a food figure into joules with the small-c factor and land three orders of magnitude low. If you are working with intake rather than units, the calorie calculator works in food Calories throughout and never asks you to make this conversion at all.
Every conversion goes through the joule
Eleven units could be connected by 121 direct factors, and a table that size cannot be kept consistent. Instead each unit is stored as one number — how many joules it is — and every conversion is two steps.
joules = value × f(from) • result = joules ÷ f(to)- f(u)
- Joules in one unit u — 4.184 for the calorie
- joules
- The quantity in the SI unit
- result
- The quantity in the unit you asked for
Most of the column is exact by definition rather than measured:
- 1 cal = 4.184 J exactly — the thermochemical calorie. 1 kcal = 4,184 J, being a thousand of them.
- 1 Wh = 3,600 J, 1 kWh = 3,600,000 J. A watt is a joule per second and an hour is 3,600 seconds; that is the whole derivation.
- 1 BTU (IT) = 1,055.05585262 J exactly, and the therm follows as 100,000 of them, 105,505,585.262 J.
- 1 ft·lbf = 1.3558179483314 J exactly. The pound is exactly 0.45359237 kg, standard gravity is exactly 9.80665 m/s² and the foot is exactly 0.3048 m, so the product is exact too.
- 1 eV = 1.602176634 × 10⁻¹⁹ J exactly since 20 May 2019, when the SI redefinition fixed the elementary charge at that value rather than measuring it.
Results are rounded to twelve significant figures rather than to a fixed number of decimal places. A table spanning electronvolts to therms has no single sensible decimal place — two decimals turns every electronvolt into zero, and twenty turns a therm into binary noise. Significant figures are also what makes 1 kcal come back as exactly 1,000 cal: 4184 ÷ 4.184 in floating point is 1000.0000000000001.
One kilowatt-hour, all the way through
Step one: 1 × 3,600,000 = 3,600,000 joules. Step two divides by the target. Into kilojoules that is 3,600,000 ÷ 1,000 = 3,600 kJ. Into BTU it is 3,600,000 ÷ 1,055.05585262 = 3,412.14 BTU — the figure printed on an air conditioner’s efficiency label. Into food Calories it is 3,600,000 ÷ 4,184 = 860.4 kcal, which is a decent restaurant main course.
Read that last line the other way and it is the more useful comparison: a 2,000 Calorie day is about 2.32 kWh (2,000 × 4,184 = 8,368,000 J, ÷ 3,600,000 = 2.324). At a US average retail electricity price near 17 cents per kWh, a day’s food energy costs about 40 cents as electricity. Food is not electricity and the comparison proves nothing about diet — but it does anchor two units most people hold in completely separate mental compartments.
And a demonstration that the factors really are exact: convert 1 therm and read the table. BTU says 100,000 exactly, because that is what a therm is defined as. Convert 1 kcal and the calorie row says 1,000 exactly. Neither is a rounded result that happens to land on a round number — they are definitions, arriving back intact.
What this converter assumes
- The calorie is the thermochemical one, 4.184 J exactly, and the BTU is the International Table one, 1,055.05585262 J exactly. If your source specifies a different calorie or a different BTU, the answers here will differ in the fourth significant figure.
- The therm is 100,000 BTU (IT). A United States gas bill’s therm is 0.024% smaller. Use this tool for physics and engineering; use the number printed on the bill for the bill.
- Negative values are accepted, because an energy change is signed: a combustion enthalpy is negative and a bond dissociation energy is positive. If you are converting a magnitude, the sign simply never appears.
- Nothing here converts energy into power, into mass, or into a quantity of fuel. A watt is a joule per second, E = mc² is a physics claim rather than a unit conversion, and a “tonne of TNT” is a convention about a representative explosive. All three are deliberately absent.
- Results carry twelve significant figures internally and are displayed to ten. Neither is a claim about your measurement — a meter reading good to 0.1 kWh is still good to 0.1 kWh after conversion.
Energy conversion FAQ
Is a Calorie the same as a calorie?
No — and the gap is a factor of a thousand. The Calorie with a capital C on a nutrition label is a kilocalorie: 1,000 of the calories a physicist or chemist means, or 4,184 joules. A 2,000 Calorie day is 2,000 kcal, which is 2,000,000 small calories, 8.368 megajoules, or about 2.32 kilowatt-hours. Both units get spoken as "calories" and both get abbreviated "cal" by somebody, which is why this converter lists them as two separate entries and prints both alongside every answer.
Which calorie does this use — there are several?
The thermochemical calorie, defined as exactly 4.184 joules. It is the one behind nutrition labelling and the one chemistry uses. The other three in circulation are the International Table calorie (4.1868 J), the 15 °C calorie (about 4.1855 J) and the mean calorie (about 4.190 J). The spread is roughly 0.15% — invisible in a meal, and enough to fail a calorimetry check.
Which BTU does this use?
The International Table BTU, exactly 1,055.05585262 joules. That is the BTU meant by an appliance rating or an HVAC sizing figure. At least four others exist, because a BTU is the heat needed to raise a pound of water by one degree Fahrenheit and water's heat capacity depends on which degree: the thermochemical BTU is 1,054.350 J, the 59 °F BTU is 1,054.804 J and the 39 °F BTU is about 1,059.67 J.
How many joules is one kilowatt-hour?
Exactly 3,600,000 J, or 3.6 megajoules. A watt is a joule per second, so a kilowatt sustained for 3,600 seconds delivers 1,000 × 3,600 joules. There is nothing approximate about it — the only reason the number looks arbitrary is that the hour is a sexagesimal survivor in a decimal system.
Is the therm here the same as the therm on my gas bill?
Probably not exactly. This tool uses the therm defined as exactly 100,000 BTU (IT), which is 105,505,585.262 J — the value NIST lists as therm (EC). A United States gas bill uses the therm (U.S.), 105,480,400 J, built on the 59 °F BTU instead. The difference is 0.024%, which on a 100-therm winter month is about a fortieth of a therm. It matters for reconciliation to the penny and for nothing else.
What is an electronvolt doing in the same list as a therm?
Demonstrating range. An electronvolt is exactly 1.602176634 × 10⁻¹⁹ J — the energy one electron gains crossing one volt — and a therm is about 1.06 × 10⁸ J. That is 27 orders of magnitude in one table, which is why results here are rounded to significant figures rather than decimal places, and why anything past a trillion or under a millionth is printed in scientific notation.
Can I convert a kilowatt into kilowatt-hours?
Not directly, and the tool deliberately does not offer it. A kilowatt is a rate — a kilojoule every second. A kilowatt-hour is a quantity. To get from one to the other you need a duration: a 2 kW heater run for 90 minutes uses 2 × 1.5 = 3 kWh. Putting power and energy in the same menu is how that confusion spreads, so this converter keeps to energy.
Sources and review notes
- NIST Special Publication 811 — Guide for the Use of the International System of Units (SI). Appendix B lists every factor used here, including all four calories, all five BTUs and both therms
- BIPM — The International System of Units (SI) Brochure, for the joule and for the 2019 redefinition that fixed the elementary charge, and with it the electronvolt
- NIST — CODATA value of the electronvolt-joule relationship, now an exact defined quantity rather than a measured one
These factors are defined values rather than measured ones, so they do not go stale: the thermochemical calorie is fixed at 4.184 J by definition, and the electronvolt stopped being a measured quantity in 2019. The only figure on this page that could move is the electricity price in the worked example, which is illustrative and not part of any calculation.