Energy Converter
Joules, calories, kWh and BTU.
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Result
4.184 kJ
1 kilocalorie (food calorie) in kilojoule
1 kcal = 4.184 kJ
Energy Conversion Math Formula
Energy is the capacity to do work, and its units come from very different places: mechanics (the joule and the foot-pound), heat (the calorie and the BTU) and electricity (the watt-hour and the kilowatt-hour). They all measure the same physical quantity, so each one is a fixed multiple of the joule. Converting is a matter of multiplying by a fraction equal to 1.
The part that trips people up is the watt-hour. A watt is a joule per second, so a watt-hour is a joule per second held for 3,600 seconds: 1 Wh = 3,600 J. That makes 1 kWh = 3,600,000 J = 3.6 MJ. The converter goes through joules.
The formula
value in B = value in A × (J per A) ÷ (J per B)Energy (J) = Power (W) × Time (s)1 Wh = 3,600 J, 1 kWh = 3,600,000 J, 1 kcal = 4,184 J
Worked example 1: A 2,000 kcal diet, in kilojoules
2,000 kcal × (4,184 J ÷ 1 kcal) = 8,368,000 J8,368,000 J × (1 kJ ÷ 1,000 J)Answer: 8,368 kJ
Food labels in many countries print both figures. The ratio between them is always 4.184.
Worked example 2: One kilowatt-hour, in kilocalories
1 kWh × (3,600,000 J ÷ 1 kWh) = 3,600,000 J3,600,000 J × (1 kcal ÷ 4,184 J)Answer: 860.421 kcal
That is about the food energy of a large dinner, released as heat by a 1,000 W heater in a single hour.
Worked example 3: A 60 W bulb left on for 5 hours, in kWh
60 W × 5 h = 300 Wh300 Wh × (1 kWh ÷ 1,000 Wh)Answer: 0.3 kWh
In joules that is 300 × 3,600 = 1,080,000 J, or 1.08 MJ. Multiply the kWh figure by your price per unit and you have the cost on the bill.
Worked example 4: 5 kWh, in BTU
5 kWh × (3,600,000 J ÷ 1 kWh) = 18,000,000 J18,000,000 J × (1 BTU ÷ 1,055.05585262 J)Answer: 17,060.7 BTU
The BTU used here is the International Table BTU. Other BTU definitions exist and differ from it by a fraction of a percent.
Common mistakes to avoid
- Mixing up kW and kWh. A kilowatt (kW) is power, a rate. A kilowatt-hour (kWh) is energy, an amount. A 2 kW heater that runs for 3 hours uses 6 kWh. Bills are in kWh, appliance ratings are in kW.
- Calorie against Calorie. A small calorie (cal) is 4.184 J. A food Calorie, written with a capital C or as kcal, is 1,000 of them: 4,184 J. When a label says 200 Calories it means 200 kcal. Dropping the factor of 1,000 makes the number a thousand times too small.
- Using 3,600 when you needed 3,600,000. Watt-hours to joules: multiply by 3,600. Kilowatt-hours to joules: multiply by 3,600,000. The extra three zeros are the kilo.
About energy units
The joule is the SI unit of energy: the work done by a force of one newton over one metre, or the energy a 1 watt device uses in one second. Lifting a small apple from the floor to a tabletop takes roughly one joule.
The other units survive because each one fits its field. Dietitians use the kilocalorie and the kilojoule, electricity suppliers use the kilowatt-hour, US heating and cooling use the BTU, and engineers in imperial countries still quote foot-pounds. Each one is defined as an exact multiple of the joule, which is how this tool converts them.
- Joule (J)One newton metre, or one watt for one second. The SI unit.
- Kilojoule (kJ)1 kJ = 1,000 JA thousand joules. Printed on food labels in the EU, Australia and many other places.
- Calorie (cal)1 cal = 4.184 JThe thermochemical calorie, about the heat needed to warm 1 g of water by 1 °C.
- Kilocalorie (food Calorie) (kcal)1 kcal = 4,184 JA thousand calories. This is the food Calorie.
- Watt-hour (Wh)1 Wh = 3,600 J3,600 joules. Battery capacity is often quoted in watt-hours.
- Kilowatt-hour (kWh)1 kWh = 3,600,000 J3.6 million joules. The unit on electricity bills.
- British thermal unit (BTU)1 BTU = 1,055.055853 JThe International Table BTU, about the heat needed to warm 1 lb of water by 1 °F.
- Foot-pound force (ft·lbf)1 ft·lbf = 1.355817948 JThe work of a one pound-force over one foot.
Energy conversion table
| Value | J | kJ | kcal | Wh |
|---|---|---|---|---|
| 1 cal | 4.184 | 0.004184 | 0.001 | 0.00116222 |
| 1 kcal | 4,184 | 4.184 | 1 | 1.16222 |
| 1 Wh | 3,600 | 3.6 | 0.860421 | 1 |
| 1 kWh | 3,600,000 | 3,600 | 860.421 | 1,000 |
| 1 BTU | 1,055.06 | 1.05506 | 0.252164 | 0.293071 |
| 1 ft·lbf | 1.35582 | 0.00135582 | 0.000324048 | 0.000376616 |
Energy converter FAQ
How do I convert kcal to kJ?
Multiply by 4.184. 250 kcal is 250 × 4.184 = 1,046 kJ. Divide by 4.184 to go back.
How many joules are in a kilowatt-hour?
3,600,000. A kilowatt is 1,000 joules per second and an hour is 3,600 seconds, and 1,000 × 3,600 = 3,600,000.
What is the difference between a calorie and a Calorie?
A calorie with a small c is 4.184 J. A Calorie with a capital C, also written kcal, is 1,000 calories, which is 4,184 J. Food labels use the large one.
How do I work out the energy an appliance uses?
Multiply its power by the time it runs. A 900 W kettle that runs for 3 minutes (0.05 h) uses 900 × 0.05 = 45 Wh, or 0.045 kWh. Multiply by your price per kWh for the cost.
How many BTU are in a kilowatt-hour?
3,412.14. Divide 3,600,000 J by 1,055.05585 J.
How many kWh does a battery hold?
Divide its watt-hours by 1,000. A 10,000 mAh power bank at 3.7 V holds 10 Ah × 3.7 V = 37 Wh, which is 0.037 kWh.