Solve direct and inverse proportions: enter three known values and get the fourth, with the math spelled out.
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.
Direct: A/B = C/X → X = (B × C) ÷ A. Inverse: A × B = C × X → X = (A × B) ÷ C.
Ask whether the quantities move in the same direction. More distance, more fuel: direct. More speed, less time: inverse.
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.
Yes, with comma or dot as the decimal separator.
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.
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