What is the rule of three and how does it work
The rule of three is a mathematical method for solving proportion problems between quantities. If you know three related values, you can calculate a fourth unknown quickly and accurately.
It is used daily in shopping, cooking recipes, unit conversions, speed calculations, cost allocation, and any situation where one quantity varies in proportion to another. Our online rule of three calculator lets you solve these problems without errors and see every step of the calculation.
Types of rule of three: simple and compound, direct and inverse
Simple direct rule of three
Used when two quantities are directly proportional: if one increases, the other increases in the same proportion. For example, if 3 kg of apples cost €6, how much do 5 kg cost? The formula is x = (b × c) / a.
Simple inverse rule of three
Used when quantities are inversely proportional: if one increases, the other decreases. For example, if 4 workers take 6 days to finish a job, how long will 8 workers take? The formula is x = (a × b) / c.
Compound direct rule of three
Involves more than one direct proportional relationship between three or more quantities. Data is organized in columns and the formula x = (b × d × e) / (a × c) is applied. Common in problems with multiple related variables, such as production with different factors.
Compound inverse rule of three
Combines inverse relationships between multiple quantities. The formula is x = (a × b × d) / (c × e). Used when at least one relationship between quantities is inverse, such as in performance problems with different resources.
Rule of three examples in everyday life
Shopping: if 2 liters of milk cost €1.80, with simple direct rule of three you calculate the price of 5 liters: x = (1.80 × 5) / 2 = €4.50.
Speed and time: if a car at 80 km/h takes 3 hours, at 120 km/h it will take less (inverse proportion): x = (80 × 3) / 120 = 2 hours.
Recipes: if a recipe for 4 people uses 200 g of flour, for 10 people you need x = (200 × 10) / 4 = 500 g. The rule of three simplifies these calculations without complex formulas.
Frequently asked questions about the rule of three
What is the rule of three?
The rule of three is a mathematical technique to calculate an unknown value (x) from three known values that maintain a proportional relationship, either direct or inverse.
What is the difference between direct and inverse rule of three?
In direct rule of three, when one quantity increases, the other also increases proportionally. In inverse rule of three, when one increases, the other decreases. Identifying the correct type is key to applying the right formula.
How do you solve a simple rule of three?
Organize data in two rows: the first with known values (a → b) and the second with one known value and the unknown (c → x). If direct, calculate x = (b × c) / a. If inverse, x = (a × b) / c.
What is compound rule of three?
Compound rule of three applies when three or more quantities are related. Values are organized in columns and multiplied or divided depending on whether proportions are direct or inverse.
What is a rule of three calculator used for?
It solves proportion problems quickly and without errors. Besides the result, it shows the formula and calculation steps, helping you understand and learn the rule of three.
Is rule of 3 the same as rule of three?
Yes, rule of 3 and rule of three are equivalent terms. Both refer to the same proportion calculation method taught in school mathematics and used in daily life.