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Rule of three calculator

Solve a direct or inverse rule of three: if A is to B, C is to X. One of the most commonly used calculations in everyday life.

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is toasis to X

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In direct mode it calculates X = (B × C) / A (direct proportionality). In inverse mode it calculates X = (A × B) / C, because the product of both quantities stays constant (inverse proportionality).

Use cases

  • Scaling a recipe to a different number of servings.
  • Converting proportional quantities in a formula.
  • Solving school proportionality problems.

How it works

  1. 1

    Pick the type

    Direct if both quantities rise together; inverse if one rises as the other falls.

  2. 2

    Enter A and B

    Type the first two values of the known ratio.

  3. 3

    Enter C

    Type the third value and get X instantly.

Technical details

  • Example: if 3 kg cost $7.50, how much do 5 kg cost? A = 3, B = 7.50 and C = 5, so X = 7.50 × 5 / 3 = $12.50.
  • Inverse example: if 4 people take 6 days, how long do 3 take? A = 4, B = 6 and C = 3, so X = 4 × 6 / 3 = 8 days.
  • If the divisor is 0 (A in direct mode, C in inverse mode) there's no proportion to solve and the calculator shows "-". Result rounded to 4 decimal places. You can type decimals with a comma or a dot (12.5 or 12,5).

Frequently asked questions

How do I know if my rule of three is direct or inverse?

Ask what happens to the second quantity if you double the first: if it doubles too (more kilos, higher price) it's direct; if it halves (more workers, fewer days; higher speed, less time) it's inverse.

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