Rule of Three Calculator

Calculate simple rule of three, direct or inverse, in seconds. Fill in the three known values and get instant results with no registration required.

What is the rule of three?

The rule of three is a mathematical method used to find an unknown value by using a proportional relationship between two known quantities. You input three values (A, B, and C), and the calculator determines the fourth (X) while preserving the proportion between A and B.

Direct rule of three

Used when two quantities are directly proportional: as one increases, the other increases at the same rate. The formula is:

X = (B × C) ÷ A

Example: If 5 kg of a product cost $20, how much do 8 kg cost? A = 5, B = 20, C = 8, so X = (20 × 8) ÷ 5 = $32.

Inverse rule of three

Used when quantities are inversely proportional: as one increases, the other decreases. The formula is:

X = (A × B) ÷ C

Example: If 3 workers build a wall in 12 hours, how many hours will 6 workers take? A = 3, B = 12, C = 6, so X = (3 × 12) ÷ 6 = 6 hours. This makes sense: with twice as many workers, the job takes half the time.

How to know which one to use

Ask yourself: when one quantity increases, does the other increase too? Use direct. When one increases, does the other decrease? Use inverse. Speed and travel time, for example, are inversely proportional: the faster you go, the less time it takes.

Frequently asked questions

What is the rule of three?

It is a method to find an unknown value based on a proportional relationship between two known quantities. It can be direct or inverse.

What is the difference between direct and inverse rule of three?

In a direct rule of three, quantities increase together. In an inverse rule of three, one increases while the other decreases, such as more workers taking less time to complete a task.

How to tell if a rule of three is direct or inverse?

If both quantities increase together, it is direct. If one increases and the other decreases, it is inverse.