Rule of three calculator
Find the missing value in a proportion: if A corresponds to B, what corresponds to C?
Rule of three calculator: what it is and how it works
The rule of three is a method for finding an unknown value from three others when two quantities are proportional. It is direct when one quantity increases in the same proportion as the other: more kilos of fruit cost more money. It is inverse when one increases as the other decreases: more workers need fewer days to finish a job.
For a direct rule of three, X is B times C divided by A. For an inverse one, A times B divided by C. It is used every day to scale recipes, work out unit prices, convert map scales or share out working time.
How to use it
- Choose whether the proportion is direct or inverse.
- Enter the three known values: A, B and C.
- Get the value of X and the operation used.
Direct: X = B × C ÷ A · Inverse: X = A × B ÷ CWorked example
Direct: if 3 kg of apples cost €4.50, 7 kg cost 4.50 × 7 ÷ 3 = €10.50. Inverse: if 4 people take 6 days to paint a house, 3 people take 4 × 6 ÷ 3 = 8 days.
Frequently asked questions
How do I know if it is direct or inverse?
Ask what happens if one quantity doubles. If the other doubles too, it is direct; if it halves, it is inverse.
What is a compound rule of three?
One that relates more than two quantities. It can be solved by chaining several simple rules of three.
Does it work for percentages?
Yes. 15 % of 80 is a rule of three: if 100 is to 15, 80 is to X = 80 × 15 ÷ 100 = 12.
Can I use decimals?
Yes, decimals with a point or comma are accepted.