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A rule of three (Dreisatz) calculator for proportional and inverse relationships, one of the most useful everyday maths tricks and a staple of school exercises. The rule of three finds an unknown value from a known ratio.

In the proportional case, if A corresponds to B, then C corresponds to B times C divided by A, because the two quantities rise and fall together.

The inverse case is for quantities that move in opposite directions: as one goes up, the other goes down. Here, if A corresponds to B, then C corresponds to A times B divided by C, for example more workers meaning less time for a job.

Enter the known pair and the value you want to scale, choose whether the relationship is proportional or inverse, and the answer appears instantly with the calculation laid out.

Uses are everywhere: scaling a recipe up or down, working out a unit price, converting a rate, or estimating how long a task takes with more or fewer people. All four values and the result can be decimals, so it works for prices, quantities, speeds and time. Everything runs in your browser.