# Energy converter

> Convert kWh to BTU, calories to joules, kcal to kJ and therms to kWh, using the exact definitions of the joule, calorie, BTU and electronvolt.

Interactive version: https://www.calcopenly.com/conversion/energy-converter
Subject: Unit converters

Every energy unit is a fixed number of joules. A kilowatt-hour is exactly 3.6 MJ (1,000 W for 3,600 s), the thermochemical calorie is 4.184 J, and the International Table British thermal unit is 1,055.05585262 J (NIST SP 811), so each factor is a definition rather than a measurement.

The default converts 1 kWh to 3,412.14 BTU, the link between electricity bills and heating or air-conditioning ratings. Food energy is the other everyday use: a food Calorie is a kilocalorie, so a 2,000 kcal day is 8,368 kJ.

Some units share a name but not a size. The International Table calorie (4.1868 J) is 0.07% larger than the thermochemical one used here, and the US therm (105,480,400 J) is defined with the 59 °F BTU, so it comes to 99,976 International Table BTU rather than 100,000.

## Inputs

- **Value**: A number in the “from” unit, or with its own unit
- **From** (options: joule (J), kilojoule (kJ), megajoule (MJ), watt-hour (Wh), kilowatt-hour (kWh), megawatt-hour (MWh), calorie (cal), kilocalorie (kcal), British thermal unit (BTU), therm (US) (thm), electronvolt (eV), erg, foot-pound (ft·lbf), tonne of oil equivalent (toe))
- **To** (options: joule (J), kilojoule (kJ), megajoule (MJ), watt-hour (Wh), kilowatt-hour (kWh), megawatt-hour (MWh), calorie (cal), kilocalorie (kcal), British thermal unit (BTU), therm (US) (thm), electronvolt (eV), erg, foot-pound (ft·lbf), tonne of oil equivalent (toe))

## Results

- Converted value — main result
- Conversion
- Conversion factor
- Exactness

## Formula

$$
\begin{gathered} x_{\text{to}} = x_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \\ f = \text{one unit expressed in } \text{J} \end{gathered}
$$

## Worked examples

### 1 kWh in BTU

- Value: 1 kWh
- From: kilowatt-hour (kWh)
- To: British thermal unit (BTU)
- **Converted value: 3,412.14163313 BTU**
- Checked against: 3,600,000 J ÷ 1055.05585262 J (International Table BTU, NIST SP 811 App. B) (Python 3.8 fractions from the legal definitions)

### 1 kcal in kJ

- Value: 1 kcal
- From: kilocalorie (kcal)
- To: kilojoule (kJ)
- **Converted value: 4.184 kJ**
- **Exactness: Exact**
- Checked against: Thermochemical calorie = 4.184 J exactly (NIST SP 811 App. B)

### 1 eV in joules

- Value: 1 eV
- From: electronvolt (eV)
- To: joule (J)
- **Converted value: 1.602176634 × 10⁻¹⁹ J**
- Checked against: e = 1.602176634 × 10⁻¹⁹ C exactly (SI 2019), so 1 eV = 1.602176634 × 10⁻¹⁹ J

### 1 US therm in BTU

- Value: 1 thm
- From: therm (US) (thm)
- To: British thermal unit (BTU)
- **Converted value: 99,976.1289775 BTU**
- Checked against: 105,480,400 J (NIST SP 811 App. B) ÷ 1055.05585262 J (Python 3.8 fractions from the legal definitions)

## Questions

### How many BTU are in a kWh?

3,412.14 BTU. A kWh is 3,600,000 J and the International Table BTU is 1,055.05585262 J, so 3,600,000 ÷ 1,055.05585262 = 3,412.1416. In the other direction 1 BTU is 0.000293071 kWh, so 100,000 BTU of heat is 29.31 kWh.

### How many joules are in a calorie?

4.184 J for the thermochemical calorie used here, or 4.1868 J for the International Table calorie; NIST SP 811 lists both. Nutrition labels count kilocalories, often printed as “Calories”, so one food Calorie is 4,184 J or 4.184 kJ. EU food labels give energy in both kJ and kcal.

### What is a unit of electricity?

One kilowatt-hour, 3.6 MJ: the energy a 1,000 W appliance uses in one hour. Electricity bills in the UK and India count “units” in kWh, so a 2 kW heater running for 3 hours uses 6 units, and a 10 W LED bulb takes 100 hours to use one.

### What is the difference between kW and kWh?

A kilowatt measures power, the rate at which energy is used; a kilowatt-hour measures the energy itself, power multiplied by time. A 3 kW kettle running for 4 minutes uses 3 × 4/60 = 0.2 kWh. Convert kW with the power converter and kWh with this one.

### How many kWh are in a therm?

29.3 kWh. The US therm is 105,480,400 J (NIST SP 811), which is 29.3001 kWh; the EU and UK therm, 100,000 International Table BTU or 105,505,585.262 J, is 29.3071 kWh. The two differ by 0.024%, so either rounds to 29.3 kWh.

### How accurate is the energy converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 4 worked examples whose answers come from independent sources; for example, “1 kWh in BTU” is checked against 3,600,000 J ÷ 1055.05585262 J (International Table BTU, NIST SP 811 App. B) (Python 3.8 fractions from the legal definitions).

### Where does the method come from?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement.

## Sources

- [NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44, Appendix C — General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)