Energy Converter: Joules, kWh, Calories and BTU

Energy Unit Converter

Energy is the capacity to do work or produce heat. An energy unit converter rewrites an energy figure from one unit into another, such as kilowatt-hours into joules. This page converts between joules, kilojoules, calories, kilocalories, watt-hours, kilowatt-hours and BTU, and shows all seven values at the same time.

What the converter does

A visitor types one number and picks the unit that number is written in. The page returns the same energy in all seven units.

• Results are shown to eight significant figures. Only the display is rounded. The conversion runs on the number as typed.
• A result below 0.0001 in size, or of a billion or more, is shown in scientific notation. Zero is shown as a plain 0.
• Negative values are accepted. A reaction that absorbs heat rather than releasing it has a negative one.
• An empty box produces a prompt rather than a number. A link carrying a unit the page does not offer produces a message rather than a conversion.

The seven units

The joule is the SI unit: the work done by one newton acting over one metre. Each of the other six units is a fixed number of joules. None of those six numbers is a measurement, so none of them changes over time.

Energy conversion formula

Every unit here is a fixed multiple of the joule, so a conversion is one multiplication followed by one division. The value is carried into joules, then back out into the unit wanted:

$E_2 = \frac{E_1 \times k_1}{k_2}$

where $E_1$ is the energy typed in, $k_1$ is the number of joules in one unit of the chosen unit, $k_2$ is the number of joules in one unit of the wanted unit, and $E_2$ is the answer.

Nothing is added or subtracted along the way, because all seven scales read zero at the same energy. Only the size of the step changes. Temperature is the case where that is untrue: Celsius and Fahrenheit start counting from different points, so a converter that only multiplied would report 0 °C as 0 °F instead of 32 °F.

Where the calorie and the BTU come from

A calorie was originally the energy to raise one gram of water by one degree Celsius, but two different experiments fixed that idea at two very slightly different sizes. This page uses the thermochemical calorie, fixed at exactly 4.184 J, which is the figure used in chemistry and in food-energy labelling (1,000 of them make the kilocalorie printed as "Calories" on a nutrition label). A second, separate definition, the International Table calorie, is fixed at exactly 4.1868 J and is folded into the BTU below rather than exposed as its own unit here, because the two calories differ by about 0.06% and are easy to mix up.

The BTU on this page is the International Table BTU, the figure printed on HVAC and AC equipment. It is defined as the energy to raise one pound of water by one degree Fahrenheit, using the International Table calorie:

$1\ \mathrm{BTU} = 453.59237\ \mathrm{g} \times \frac{5}{9}\,\mathrm{K/°F} \times 4.1868\ \mathrm{J/(g \cdot K)} = 1055.05585262\ \mathrm{J}$

The 453.59237 g comes from the International Yard and Pound Agreement of 1959, which fixes the pound at exactly that many grams. The 5/9 converts a one-degree-Fahrenheit temperature difference into kelvin. All three factors are exact, so the product is exact too, and the decimal above stops rather than repeating.

Example: a 10 kWh solar battery

A home battery rated at 10 kWh stores 10,000 watt-hours. Converting to joules, the SI unit used in physics:

$E = 10 \times 3{,}600{,}000 = 36{,}000{,}000\ \mathrm{J} = 36\ \mathrm{MJ}$

Converting the same 10 kWh to BTU, the unit used to size the heating or cooling load it could run:

$E = \frac{10 \times 3{,}600{,}000}{1055.05585262} \approx 34{,}121.416\ \mathrm{BTU}$

And to kilocalories, the unit used on a food label:

$E = \frac{10 \times 3{,}600{,}000}{4184} \approx 8{,}604.2065\ \mathrm{kcal}$

For this input the page shows 36,000,000 J, 36,000 kJ, 8,604,206.5 cal, 8,604.2065 kcal, 10,000 Wh, 10 kWh and 34,121.416 BTU side by side.

Common energy conversions

Each row shows what one unit of the left-hand column comes to in each of the seven units, at eight significant figures.

Which values are exact and which are rounded

Every unit here rests on a definition, but only some of those definitions can be written out in full as decimals.

• 1 kJ is exactly 1,000 J. Kilo is the SI prefix for a thousand.
• 1 cal is exactly 4.184 J, and 1 kcal is exactly 4,184 J. Both decimals stop.
• 1 Wh is exactly 3,600 J, and 1 kWh is exactly 3,600,000 J: a watt is a joule per second, and an hour is 3,600 seconds, both exact.
• 1 BTU is exactly 1,055.05585262 J, composed from three exact definitions rather than stored as a shortened decimal.

The converter builds the BTU figure from its defining constants rather than storing a rounded number, so the rounding a reader sees comes from the display and not from the numbers behind it. Eight significant figures is wide enough to show a defining value clearly and narrow enough to hide the last digits of the computer's arithmetic, which carry rounding noise rather than information.

Frequently asked questions

How many joules is one kilowatt-hour? Exactly 3,600,000 J, or 3.6 MJ. A kilowatt-hour is the energy used by a one-kilowatt appliance running for one hour, and the number follows directly from the second being 1/3,600 of an hour.

Is a calorie the same everywhere? No. This page uses the thermochemical calorie (4.184 J), the figure used in chemistry and folded into food-energy kilocalories. The International Table calorie (4.1868 J), used to define the BTU below, is a separate, later definition about 0.06% larger.

How is kWh converted to BTU? Divide the kilowatt-hours by 0.00029307107, or multiply by about 3,412.14. One kilowatt-hour is 3,412.1416 BTU.

What is a food Calorie in joules? A food "Calorie" (capital C) is a kilocalorie: exactly 4,184 J, or about 4.184 kJ. A 250-Calorie snack carries about 1,046 kJ.

Can a negative energy be converted? Yes. Energy is signed, so a value below zero describes energy flowing the other way, such as a reaction absorbing heat instead of releasing it. The page converts it rather than refusing it.

Why are so many digits shown? Eight significant figures keeps a defining value legible without showing the last digits of the arithmetic, which carry rounding noise. The stored constants are never shortened, so a shorter display never feeds back into the next conversion.