Rule of Three
Solve the rule of three instantly. Calculate direct proportions quickly and for free.
If A is to B, then C is to X
What is the rule of three
The rule of three is a mathematical method to solve proportionality problems when three values are known and you want to find a fourth. It is used a lot in everyday life: cooking recipes, unit conversions, mixture ratios and many practical calculations.
The formula
X = (B × C) ÷ A
If A is to B as C is to X, then X is calculated by multiplying B by C and dividing by A. For example, if 2 kg cost €4, 6 kg will cost (4 × 6) ÷ 2 = €12.
Real examples
- Cooking: if a recipe for 2 people uses 200 g of flour, for 5 people you will need (200 × 5) ÷ 2 = 500 g.
- Travel: if a car uses 6 litres every 100 km, over 250 km it will consume (6 × 250) ÷ 100 = 15 litres.
- Shopping: if 3 items cost €9, 7 items will cost (9 × 7) ÷ 3 = €21.
Direct and inverse rule of three
This calculator solves the direct rule of three, in which two quantities increase or decrease together (more quantity, more cost). There is also an inverse rule of three, in which when one quantity increases the other decreases; for example, the more workers, the fewer days it takes to finish a job.
How it relates to percentages
A percentage is nothing more than a case of the rule of three: if the total equals 100%, any percentage is a proportional part of that total. This is why this tool relates to the percentage calculator and the VAT calculator.