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Arithmetic, time and navigation

Rule of three

Direct (proportional) or inverse rule of three from three known values.

First known value, in the same quantity as C.

Known value that corresponds to A.

Second value, in the same quantity as A.

Result

X (the value that corresponds to C)
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How it is calculated

Direct: A is to B as C is to X, so X = C × B ÷ A. Example: a recipe with 2 eggs (A) needs 3 cups of flour (B); with 4 eggs (C), it needs X = 4 × 3 ÷ 2 = 6 cups.

Inverse: A × B = C × X, so X = A × B ÷ C. Used when a larger quantity of one thing makes the other smaller. Example: 4 workers (A) build a wall in 6 days (B); with 8 workers (C) it takes X = 4 × 6 ÷ 8 = 3 days (the total work, 24 worker-days, is shared among more people).

Keep in mind

  • Check that the relationship is really direct or inverse before calculating: many quantities (for example the output of a tired team) are not exactly proportional.
  • A and C must share the same units, and likewise B and X.

See also

More tools in “Arithmetic, time and navigation”