Conversions

Why a conversion is worth a tool at all

Because most of the errors are not arithmetic. They are definitional: two units with the same name that are not the same size, or a ratio published to five figures and used at three. Multiplying correctly by the wrong constant produces an answer that looks entirely plausible and is out by twenty per cent.

The fuel figures are the clearest case on the site. A US gallon is 3.785411784 litres and an imperial gallon is 4.54609 litres — twenty per cent larger — so the same consumption expressed in litres per 100 km becomes a twenty per cent different miles-per-gallon figure depending on which gallon was meant. Twenty per cent is the whole margin between two cars looking close and one looking clearly better. Every tool here that touches a gallon says which one it used.

Exact, conventional, and the difference between them

Some conversions are exact by definition and some are averages that vary with the physical thing being measured. Mixing the two up is how a recipe converter ends up implying a precision it cannot have, so the tools here keep them apart and say which they are giving you.

• Exact by definition: length, mass and volume between the metric and customary systems are fixed ratios agreed internationally, so they convert without loss and are reversible.
• Conventional: cup-to-gram weights for ingredients are averages, because how tightly flour is packed changes the answer by more than any rounding will. A gram figure from a volume measure is a guide, not a standard.
• Scheme-dependent: shoe sizes are not a unit system at all. US, UK and EU sizes are different manufacturer conventions with no single conversion, which is why the tool shows the foot length in centimetres alongside them — that is the only measurement in the row that means anything on its own.

The two that are not really conversions

Two tools sit here because that is where people look for them rather than because they convert units. The percentage calculator answers the five separate questions that all get called "percentage" — what is X% of Y, X is what percent of Y, the percent change from one number to another, increase a number by X%, and decrease it by X% — which are five formulas people routinely reach for the wrong one of.

The tip calculator splits a bill as well as taking a percentage of it, and it has to be explicit about two things no formula settles: which number the percentage is taken on, and how a shared bill rounds when the split does not come out even. It works on the figure you type, and says so — if the total you enter already has sales tax in it, a twenty per cent tip is more than twenty per cent of the food. The arithmetic is trivial. The conventions are not, and they differ between countries.