Energy Converter

Converting energy: the factors, and which ones are exact

This converter handles 9 energy units, all of them passing through J. Below are the factors it uses, so you can check any result by hand — and a note on which of them are exact by definition and which are conventions that depend on conditions.

How it works

• Converts between every pair of energy units at once, rather than one pair at a time.
• Uses the defined values, not rounded approximations — an inch is exactly 0.0254 m, not 0.0254001.
• Routes everything through J, so adding a unit cannot break the existing pairs.
• Marks units whose factor depends on conditions, instead of presenting a convention as a constant.

every unit converts through J

  Joules (J)                   1
  Kilojoules (kJ)              1000
  Calories (cal)               4.184   (thermochemical calorie)
  Kilocalories (kcal)          4184   (the Calorie on food labels)
  Watt-hours (Wh)              3600
  Kilowatt-hours (kWh)         3600000
  British thermal units (BTU)  1055.05585262   (International Table BTU)
  Foot-pounds (ft·lb)          1.35581794833
  Electronvolts (eV)           1.602176634e-19

to convert: value x factor(from) / factor(to)

Worked example

A worked energy conversion, step by step.

1. start 1 Kilowatt-hours (kWh)
2. to the base unit 1 x 3600000 = 3600000 J
3. into the target 3600000 / 1
4. result 3600000 Joules (J)

Multiplying into the base unit and dividing out again is the whole method. It is worth doing once by hand, because it shows that a converter is only ever as good as its factors — and that a wrong factor produces a plausible-looking number rather than an obvious error.

Reading the result

• The word calorie means two different things, differing by a factor of a thousand. The calorie on a food label is really a kilocalorie — 4,184 joules — while the scientific calorie is 4.184 joules. A 500-Calorie meal is 500 kcal, or about 2.1 megajoules, which is why nutrition labels in most of the world print kJ alongside and why the two rows here are kept clearly apart.
• Most of these factors are exact by international agreement rather than measured. The inch, the pound, the nautical mile and the standard atmosphere all have defined values, which is why the tool can show a conversion landing on a round number and be right rather than lucky.
• Results are rounded for display, not in the arithmetic. Conversions run at full double precision and only the printed value is shortened, so chaining conversions here does not accumulate rounding error the way copying rounded figures between steps would.

Common questions

Why does my result differ slightly from another converter?

Almost always because the other one rounded a factor. A converter that stores a US gallon as 3.7854 litres rather than 3.785411784 will drift in the fourth significant figure, and the drift compounds if you convert twice. Check a defined value you know — a US gallon should come out as exactly 231 cubic inches — and the rounded converter will show it as 230.99 or 231.01.

Does converting through a base unit lose accuracy?

Not meaningfully. Two floating-point operations instead of one adds error in the sixteenth significant figure, far below anything you would measure. What it buys is consistency: every pair uses the same two factors, so the table cannot contain a pair that disagrees with the rest of it.