Free calculator
Rule of three
Direct and inverse proportion without setting up an equation: enter three known values and the calculator works out the fourth as you type.
Direct proportion
The more, the more; say 3 units cost 81 Kč, how much do 7 units cost?
- Value for C
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Inverse proportion
The more, the less; say 4 workers manage it in 6 hours, how long will it take 8 workers?
- Value for C
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How the rule of three works
The rule of three solves problems where you know three values and are looking for the fourth. First you need to decide what kind of proportion it is:
- Direct proportion: when one value rises, the other rises too. More units cost more money. Calculation: X = B / A × C.
- Inverse proportion: when one value rises, the other falls. More workers means less time. Calculation: X = A × B / C.
A direct proportion example
If 5 kg of apples cost 200 Kč, how much do 8 kg cost? Into the calculator: A = 5, B = 200, C = 8. Result: 200 / 5 × 8 = 320 Kč.
An inverse proportion example
A construction job takes 10 workers 30 days. How long will it take 15 workers? Into the calculator: A = 10, B = 30, C = 15. Result: 10 × 30 / 15 = 20 days.
Who invented the rule of three
No one in particular, it developed gradually. The Egyptians and Babylonians already used ratios in construction and trade, Euclid worked with them in the Elements, the Indian mathematician Bhāskara II described the "rule of three", and translations of Arabic texts brought it to Renaissance Europe; Luca Pacioli popularised it in Summa de Arithmetica (1494).
Where the rule of three helps today
Recalculating a price for a different quantity, scaling a recipe to more portions, fuel consumption for a longer route, currency conversion, material for a bigger job, or estimating "how much will we make if we put twice as much into advertising". Anywhere two quantities rise or fall together.
Where to go next
You can do the maths. But what next? How to turn customers who bought once into customers who buy repeatedly is the subject of the book Opakovaný prodej.