Rule of Three Calculator

Solve direct and inverse proportions: enter three known values and get the fourth, with the math spelled out.

How to use

  1. Choose the type: direct (quantities grow together) or inverse (one grows while the other shrinks).
  2. Fill the three known values: A corresponds to B, and C corresponds to the unknown X.
  3. The result appears instantly with the proportion written out, so you can check the reasoning.

About this tool

The rule of three solves the most common everyday math problem: three values are known, one is missing, and the quantities are proportional. If 3 kg of rice cost R$ 21, how much do 5 kg cost? If a job takes 6 workers 10 days, how long with 4 workers? The first is a direct proportion, the second is inverse — and telling them apart is the whole trick.

In a direct proportion the quantities move together: more kilograms, more money. The unknown is X = (B × C) ÷ A. In an inverse proportion one quantity grows while the other shrinks: more workers, fewer days. There the product stays constant, so X = (A × B) ÷ C. This calculator handles both and always shows which formula was applied, with your numbers in place.

A quick sanity check helps catch the classic mistake: before computing, ask "if C is bigger than A, should X be bigger or smaller than B?". If bigger, the proportion is direct; if smaller, inverse. The written-out result below the answer makes this check automatic.

The formula

Direct: A/B = C/X → X = (B × C) ÷ A. Inverse: A × B = C × X → X = (A × B) ÷ C.

Frequently asked questions

How do I know if a proportion is direct or inverse?

Ask whether the quantities move in the same direction. More distance, more fuel: direct. More speed, less time: inverse.

Can I use it for percentages?

Yes — a percentage is a direct proportion where one side is 100. "X is what % of Y" is the rule of three 100 → Y, X → ?. The percentage calculator does it in one step.

Does it accept decimals?

Yes, with comma or dot as the decimal separator.

What about compound rule of three (three or more quantities)?

Chain it: solve one pair at a time, using each result as the new known value. Multiply the ratios of every quantity that affects the result.

Related tools

Long links? Shorten them for free

Vai.la turns any URL into a short link with click statistics, QR Code and your own biolink.

Vai.la is not responsible for how the tools are used or for decisions made based on their results.