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Rule Of Three

The Rule of Three Calculator solves direct and inverse proportion problems with three known values to find the fourth. If A is to B as C is to X, this tool finds X instantly. The rule of three is fundamental to ratio problems in everyday life — scaling recipes, currency conversion, speed-distance-time, and percentage calculations.

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About the Rule of Three Calculator

The Rule of Three Calculator solves direct and inverse proportion problems with three known values to find the fourth. If A is to B as C is to X, this tool finds X instantly. The rule of three is fundamental to ratio problems in everyday life — scaling recipes, currency conversion, speed-distance-time, and percentage calculations.

How to use it

  1. Enter three known values in the proportion: A, B, and C.
  2. Select whether the proportion is direct (more A = more X) or inverse.
  3. Click Calculate to find the unknown fourth value X.
  4. See the full proportion statement and verification.

Formula & methodology

Direct proportion: A/B = C/X, therefore X = (B * C) / A. Inverse proportion: A * B = C * X, therefore X = (A * B) / C. Cross multiplication: if A:B = C:X then A * X = B * C. Percentage: (part/whole) = (percent/100), solve for unknown. Scaling: new_amount = (new_base / old_base) * old_amount.

Common use cases

  • Scaling recipes: if 3 cups makes 12 cookies, how much for 20 cookies?
  • Currency exchange: if $100 = 92 euros, what is $350 in euros?
  • Speed problems: if 60 km in 1 hour, how far in 2.5 hours?
  • Percentage: if 25 is X% of 200, what is X?
  • Construction: if 5 workers finish in 10 days, how long for 8 workers?

Frequently asked questions

Direct proportion: as one quantity increases, the other increases proportionally. More workers = more work done. More speed = more distance covered. Inverse proportion: as one quantity increases, the other decreases proportionally. More workers = less time to complete. More speed = less time for same distance. The key test: double one variable — does the other double (direct) or halve (inverse)?
The rule of three assumes a perfect proportional relationship. In real life, proportions are approximations. Doubling a recipe may not double the cooking time (inverse proportion approximation). Doubling a workforce does not always halve completion time (communication overhead, limited resources). Use the rule of three for estimates and simple scaling, then verify with domain knowledge when precision matters.

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