Energy Converter
Energy Converter
Joules, calories, kilowatt-hours and the capital C
Energy has more units in common use than any other quantity on this site, because each field kept the one that made its own numbers convenient. Physics uses joules, nutrition uses kilocalories, electricity billing uses kilowatt-hours, and North American heating and cooling uses BTU. They all measure the same thing.
The notorious ambiguity is the calorie. A calorie with a lowercase c is 4.184 joules, the energy to heat one gram of water by one degree. A Calorie with a capital C, which is what food labels mean, is a kilocalorie: 1,000 of those, or 4,184 joules. A 500 Calorie meal contains 500 kilocalories. The capital letter is doing a thousand-fold amount of work, and most writing drops it.
Formulas
Worked examples
| From | To | Result |
|---|---|---|
| 1 kcal | J | 4,184 J |
| 2,000 kcal | kJ | 8,368 kJ |
| 1 kWh | J | 3,600,000 J |
| 1 kWh | kcal | 860.421 kcal |
| 12,000 BTU | kWh | 3.51685 kWh |
Results are computed with the same factors the converter above uses, rounded to six significant figures.
Common energy figures
| kcal | kJ | kWh |
|---|---|---|
| 100 | 418.4 | 0.116222 |
| 250 | 1,046 | 0.290556 |
| 500 | 2,092 | 0.581111 |
| 2,000 | 8,368 | 2.32444 |
| 2,500 | 10,460 | 2.90556 |
2,000 kcal is the reference daily intake used on most food labelling.
Worth knowing
- 1 thermochemical calorie = 4.184 J exactly. There is also an "international table" calorie of 4.1868 J; the difference is 0.07% and rarely matters.
- 1 kWh = 3.6 MJ exactly, because a kilowatt is 1,000 joules per second and an hour is 3,600 seconds.
- 1 BTU ≈ 1,055.06 J. It is the energy to raise one pound of water by one degree Fahrenheit, and it survives in air conditioning and boiler ratings.
- European food labels give both kilojoules and kilocalories. A 2,000 kcal daily figure is 8,368 kJ, which is why the kJ numbers on packaging look so much larger.
Frequently asked questions
- Is a food Calorie the same as a calorie?
- No. It is a thousand of them. The Calorie on a nutrition label is a kilocalorie, 4,184 joules. The scientific calorie is 4.184 joules. The convention is that a capital C means kilocalorie, but the distinction is lost constantly in ordinary writing, so treat any food figure as kilocalories.
- How many joules are in a kilowatt-hour?
- 3,600,000 joules, or 3.6 megajoules. A watt is one joule per second, so a kilowatt sustained for the 3,600 seconds in an hour delivers 3.6 million joules. This is the unit your electricity meter counts.
- What is a BTU and why do air conditioners use it?
- A British thermal unit is the energy needed to raise one pound of water by one degree Fahrenheit, about 1,055 joules. It survives in North American heating and cooling because the whole industry sized its equipment in BTU per hour long before metrication, and the ratings have never been restated.
- How many calories is one kilowatt-hour?
- About 860 kilocalories. That is a useful sanity check on domestic energy: running a 1 kW heater for an hour releases roughly the food energy of a large meal.