Energy: one quantity, nine units
| Unit | Joules | Where it is used |
|---|---|---|
| Joule (J) | 1 | The SI unit; everything else is defined from it |
| Calorie, thermochemical (cal) | 4.184 | Chemistry; the "small" calorie |
| Calorie, International Table (cal IT) | 4.1868 | Steam tables and older engineering work |
| Food Calorie = kilocalorie (kcal) | 4,184 | Nutrition labels, diet and exercise |
| British thermal unit (Btu IT) | 1,055.056 | Heating, cooling and gas in the US |
| Watt hour (W·h) | 3,600 | Batteries and small devices |
| Kilowatt hour (kWh) | 3.600 × 10^6 | Electricity bills |
| Therm (US) | 1.055 × 10^8 | Natural gas bills in the US |
| Foot pound-force (ft·lbf) | 1.3558 | Mechanical work in US units |
NIST marks some factors as exact by definition: the thermochemical calorie is exactly 4.184 J, the International Table calorie exactly 4.1868 J, and the kilowatt hour exactly 3.6 million joules. The BTU and the therm are measured conversions with a few more decimals. The energy converter applies the table in any direction.
The calorie problem
Two things called a calorie differ by a factor of a thousand. The small calorie, the chemist's unit, is about 4.18 joules. The food Calorie, written with a capital in careful texts and without one on most labels, is a kilocalorie: 1,000 small calories, 4,184 joules on the thermochemical definition that nutrition uses. The FDA's Nutrition Facts label, which uses 2,000 calories a day as its general guide, means kilocalories throughout; so does the calorie calculator. Outside the US the label shows kilojoules too, and 2,000 kcal is 8.37 MJ. There are even two small calories: NIST lists the thermochemical calorie at 4.184 J and the International Table calorie at 4.1868 J, a difference of 0.07 percent that matters in a laboratory and nowhere else.
Power: energy per time
A furnace rated at 80,000 BTU is really 80,000 BTU per hour, a rate; an air conditioner's tons are a rate too. Power units convert to watts:
| Unit | Watts | Where it is used |
|---|---|---|
| BTU per hour | 0.2930711 | Furnaces, boilers, air conditioners in the US |
| Ton of refrigeration (12,000 BTU/h) | 3,516.853 | Air conditioning capacity |
| Horsepower (550 ft·lbf/s) | 745.6999 | Engines in the US and UK |
| Metric horsepower (PS) | 735.4988 | Car engines in continental Europe |
| Electric horsepower | 746 | Electric motor ratings, exact by definition |
The power converter handles these, and the BTU calculator sizes heating and cooling for a room. Multiply a power by a time and you are back to energy: a 1,500-watt heater running for 2 hours uses 3 kWh, and the electricity cost calculator turns that into money at your tariff. The kW vs kWh guide explains the distinction with a bill, and the volts, amps and watts guide shows where the watts come from.
Comparisons that make the sizes real
- One kilowatt hour is 860 kcal of food energy or 3,412 BTU of heat.
- A 2,000-kcal day is 2.32 kWh: the energy a person runs on is about what a small space heater draws in two hours.
- One therm of gas is 100,000 BTU, 29.3 kWh. A gas bill in therms and an electricity bill in kWh can be compared once both are in the same unit.
- One ton of cooling removes 12,000 BTU per hour, 3.52 kW of heat. The electricity it uses is less, by the unit's efficiency ratio.
- One horsepower is 746 W; a 100-horsepower engine at full output is 74.6 kW.
Energy = power × time. 1 kWh = 1,000 W × 3,600 s = 3,600,000 J.
Which unit when
- Food and exercise: kilocalories, called Calories on US labels, with kilojoules alongside elsewhere.
- Electricity: kilowatt hours on the bill, watts on the appliance.
- Heating, cooling and gas in the US: BTU per hour for equipment, therms for gas; kilowatts and kilowatt hours elsewhere.
- Engines: horsepower in the US and UK, kilowatts or metric horsepower in Europe; the metric and mechanical horsepower differ by 1.4 percent.
- Science: joules, always.
Frequently asked questions
Is a food Calorie the same as a calorie?
No. The calorie used in chemistry is the energy to warm one gram of water by one degree, about 4.184 joules in NIST's thermochemical definition. The Calorie on a food label is a kilocalorie, a thousand of those, 4,184 joules. A 2,000-Calorie diet is 2,000 kcal, which is 8.4 megajoules; labels outside the US print the kilojoule figure beside it.
How many calories are in a kilowatt hour?
About 860 kilocalories, from NIST's factors of 3.6 million joules per kWh and 4,184 joules per kcal. Put the other way, a day's food energy of 2,000 kcal is about 2.32 kWh, roughly what a small heater uses in two hours.
What is a BTU?
The British thermal unit, the energy to warm one pound of water by one degree Fahrenheit; NIST gives the International Table BTU as 1,055.056 joules. It survives in the US for heating and cooling, where equipment is rated in BTU per hour, and for natural gas, where a therm is 100,000 BTU.
What is the difference between a kW and a kWh?
A kilowatt is power, the rate of using energy; a kilowatt hour is energy, a kilowatt sustained for an hour, which NIST defines as exactly 3.6 million joules. The bill charges for kWh. The kW vs kWh guide works through it with an electricity bill.
Why does an air conditioner have "tons"?
A ton of refrigeration is a rate of cooling, 12,000 BTU per hour, which NIST converts to about 3,517 watts. A 3-ton unit removes 36,000 BTU of heat per hour; it says nothing about the electricity it draws, which depends on its efficiency.
Sources
- NIST Special Publication 811, Appendix B.9: Factors for units listed by kind of quantity (calorie IT 4.1868 J and thermochemical 4.184 J, exact; kilocalorie thermochemical 4,184 J, exact; Btu IT 1,055.056 J; kilowatt hour 3.6 × 10⁶ J, exact; therm U.S. 1.054 804 × 10⁸ J; foot pound-force 1.355 818 J; Btu per hour 0.293 071 1 W; ton of refrigeration 3,516.853 W; horsepower 745.699 9 W, metric 735.498 8 W, electric 746 W)
- US Food and Drug Administration: How to understand and use the Nutrition Facts label (2,000 calories a day as the general guide; the label Calorie)