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Rule of Three Calculator

Enter three known values to calculate the fourth using a direct or inverse proportion.

X
19.2

How the rule of three works

In a direct rule of three, if A corresponds to B, then C corresponds to X, and the quantities grow in the same proportion.

In an inverse rule of three, when one quantity increases, the other decreases in the same proportion.

Direct: X = (B × C) ÷ A

The direct rule of three shows up constantly when calculating prices (if 3 kg costs €9, how much do 5 kg cost?), cooking recipes, or map scales. The inverse version shows up in work-sharing problems, speed and time, or flow rate and filling time.

Inverse: X = (A × B) ÷ C

Worked example

If 5 workers take 12 days to finish a job, how long will 8 workers take? This is inverse: X = (5 × 12) ÷ 8 = 7.5 days. On the other hand, if 3 kg of apples cost €9, 5 kg costs (9 × 5) ÷ 3 = €15 (direct rule).

Frequently asked questions

When is the direct rule of three used?
When both quantities increase or decrease together, for example price and quantity of a product.
When is the inverse rule of three used?
When one quantity increasing makes the other decrease, for example the number of workers and the time it takes.
Can I use decimals?
Yes, all fields accept decimal values.
How do I tell if a problem is direct or inverse?
Ask whether increasing one quantity also increases the other (direct) or decreases it (inverse). For example, more hours worked usually means more output (direct), but more workers usually means less time needed (inverse).
Does this work for percentages?
Yes, calculating a percentage is a specific case of the direct rule of three where one of the known values is 100.

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