Rule of Three Calculator
Solve a simple rule of three online. Enter three values and automatically calculate the fourth.
How does the rule of three work?
Faced with a proportion like A:B = C:X, the simple rule of three isolates the unknown term using X = (B × C) / A. That is why it shows up in proportional prices, speeds, mixtures, recipes and any quantity that grows in step with another.
Take a practical case. If 2 kg cost R$ 4, how much is 6 kg? Just work out X = (4 × 6) / 2 = 12.
Rule of three: simple, inverse and compound
The rule of three is the practical application of proportions to find a fourth value when three are known. In the simple direct rule, two quantities vary in the same direction — more of one means more of the other. Example: a car at 80 km/h travels 240 km in 3 h; how much will it travel in 5 h? Set up 3/240 = 5/x, cross-multiply, and find x = (5·240)/3 = 400 km. The general formula is a/b = c/x → x = (b·c)/a.
In the simple inverse rule, the quantities vary in opposite directions — more of one means less of the other. Classic example: 4 workers finish a job in 12 days; how long will 6 workers take? You cannot cross-multiply directly — first invert one of the ratios, then solve: 4/6 = x/12 → x = 8 days. To identify the case, ask: doubling input A, does B double (direct) or halve (inverse)?
Compound rule of three
When three or more quantities are involved, use the compound rule. Example: 8 workers, working 6 h/day, produce 200 parts in 5 days; how many parts will 12 workers produce working 8 h/day for 10 days? Set up the table, check the direction of each variable relative to the unknown, invert the inverse ratios, then multiply them all to find the unknown. Compound rule is essential in industrial planning, civil engineering and logistics.
FAQ
How do I tell if it is direct or inverse? Imagine doubling one of the values. If the other doubles too, it is direct. If it halves, it is inverse. Pay close attention — getting this wrong reverses the answer.
Does the compound rule always work? Only when the relations between the variables are independently proportional. Tasks involving non-linear gains (learning curves, scale economies) require more advanced models.
Can I use the rule of three with percentages? Yes — percentage is just a ratio with denominator 100. "20% of 80" is solved as 20/100 = x/80 → x = 16.
Where is the rule of three used in everyday life? Calculating travel time, scaling recipes, converting currency or units, mixing solutions, dosing medication and almost any quick estimate involving two related quantities.
Solve a rule of three
Few calculations are as useful day to day as the rule of three. You start from three values that relate proportionally and work out the fourth. This tool solves the simple rule of three and finds the missing value.
The list of uses is long. Adjusting a recipe's quantities, working out a proportional price, converting measures, estimating time or consumption. You enter the three known values and the tool calculates the fourth on its own, laying out the proportion in a way you can follow.
No setting up the cross-multiplication on paper every time. The calculation runs straight in the browser, that simple, whenever you need to solve a proportion.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.