kWh to joules

A kilowatt hour is not a strange unit, it is just a badly named one: it is a kilowatt held for an hour, and since a watt is a joule every second and an hour is 3600 seconds, one kilowatt hour is 3 600 000 joules — exactly 3.6 megajoules, with no rounding anywhere in the chain. That is why the meter on the wall counts in kilowatt hours while a physics paper counts in joules: same quantity, different size of step. This page converts between them and the other units the same quantity turns up in, and says which of those factors are exact and which are not.

How it is calculated

J = kWh × 3 600 000 · MJ = kWh × 3.6

NIST SP 811 prints the kilowatt hour to joule factor as 3.6 E+06 in boldface, and boldface in that table means the factor is exact rather than rounded. It has to be: 1000 joules per second for 3600 seconds is 3 600 000 joules by arithmetic, not by measurement. The watt hour, at 3.6 E+03, is the same statement a thousand times smaller.

Source: NIST SP 811 (2008), Appendix B.8 — kilowatt hour (kW · h) to joule (J) = 3.6 E+06

Questions people ask

Why is 1 kWh exactly 3.6 MJ and not approximately?

Because both sides are definitions. A watt is defined as one joule per second, and an hour is defined as exactly 3600 seconds — neither is a measured quantity with an uncertainty attached. Multiply them out and you get 3 600 000 joules with nothing left over. NIST prints the factor in boldface for that reason, which in its conversion tables is the mark of an exact value.

Which factors here are not exact?

One: the British thermal unit. The value used is the International Table Btu, published as 1.055 056 E+03 joules, and that is a rounded figure rather than a definition — it also has rivals, since the thermochemical Btu is 1054.350 J and there are separate ones defined at 39, 59 and 60 degrees Fahrenheit. The kilocalorie is the International Table one, 4186.8 J, and that one is exact. If a document you are working from does not say which Btu it means, the answer here may differ from it in the fourth digit.

Is a food Calorie the same as a kilocalorie?

Yes — the Calorie with a capital C on a food label is a kilocalorie, a thousand of the small calories used in physics. So a 2000 Calorie daily diet is 2000 kcal, which this page will tell you is about 8.4 megajoules, or a bit over 2.3 kilowatt hours. That last comparison is a fair unit conversion and a terrible nutritional one, since a body is not an electric heater.

How do I write the symbol?

The strictly correct form is kW · h or kW h, with a dot or a space, because it is a kilowatt multiplied by an hour. NIST notes that kWh is common practice and reflects a convention that lets the space be dropped where it causes no confusion, while itself recommending the dot. What is definitely wrong is KWH or Kwh: the k is lower case because kilo always is, and the W is capital because the watt is named after a person.

Why does the meter count kilowatt hours instead of joules?

Because the joule is far too small to bill in. A household running a steady kilowatt gets through 3.6 million joules an hour, so a quarterly bill in joules would be a number with eleven digits in it. The kilowatt hour is the same quantity in a step the size of an ordinary appliance running for an ordinary length of time, which is why the meter counts in it and the physics textbook does not.

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