Rule of three calculator
Three numbers you know, one you don’t. Fill in the table and the missing value appears, with the cross-multiplication spelled out.
Sealed on this device
Runs in your browser. Nothing is uploaded.
Sealed
Your proportion
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Read it as: A goes with B, so C goes with X.
Read it as: A goes with B, so C goes with X, the other way round.
Answer
- X
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Cross-multiplication
X = B × C ÷ A
Multiply the two values that face each other diagonally (B and C), then divide by the remaining one (A).
Multiply the two values of the first row (A and B), then divide by C.
Fill in A, B and C to find X.
How it works
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Choose the type
Direct when both quantities rise together, like weight and price. Inverse when one rises as the other falls, like speed and travel time.
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Fill in three values
Put the pair you know on the first row (A and B), and the new value on the second row (C).
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Read X
The missing value appears instantly, with the calculation written out so you can check it or copy it.
Frequently asked questions
What is the rule of three?
It is a quick way to find a missing value when two quantities are proportional. If 3 kg of apples cost 12, then 5 kg cost 12 × 5 ÷ 3 = 20.
How does cross-multiplication work?
In a proportion A/B = C/X, the products of the diagonals are equal: A × X = B × C. Dividing both sides by A gives X = B × C ÷ A.
When should I use the inverse rule of three?
When the two quantities move in opposite directions. If 4 workers need 6 days for a job, 3 workers need 4 × 6 ÷ 3 = 8 days, assuming everyone works at the same pace.
Why can’t A be zero?
In a direct proportion, the answer is divided by A, and dividing by zero has no meaning. In an inverse proportion, the same applies to C.
Does it work with decimals, percentages and negative numbers?
Yes. Type decimals with your usual separator. For percentages, enter the number without the % sign, for example 15 for 15 %.
Are my numbers sent anywhere?
No. The calculation runs in your browser and nothing is stored or uploaded.