Rule of Three Calculator
Solve direct, inverse and compound proportions instantly.
If A corresponds to B, what does C correspond to?
C → X
What is the rule of three?
The rule of three is one of the most widely used mathematical methods in everyday life. It allows you to find an unknown value from three known values that share a proportional relationship.
Direct rule of three
Used when the two quantities are directly proportional: if one increases, the other increases in the same proportion.
| Example | Problem |
|---|---|
| Recipes | If 4 people need 200g of flour, how much do 6 people need? |
| Speed and distance | If I cover 120 km in 2 hours, how far do I cover in 5 hours? |
| Map scales | If 1 cm on the map = 50 km in reality, what real distance is 3.5 cm? |
Inverse rule of three
Used when the quantities are inversely proportional: if one increases, the other decreases.
| Example | Problem |
|---|---|
| Workers and time | If 4 workers take 6 days, how long will 8 workers take? |
| Speed and time | If I take 3 hours at 60 km/h, how long at 90 km/h? |
| Pipes and filling | If 2 pipes fill a tank in 4 hours, how long do 5 pipes take? |
Compound rule of three
Used when three or more quantities are related to the result. Each quantity can be direct or inverse with respect to the value being sought.
The exponent is +1 for a direct relationship and -1 for an inverse one.
Frequently asked questions about the rule of three
When do you use the direct rule of three and when the inverse?
Use the direct rule when increasing one quantity also increases the other (more kilometres = more fuel). Use the inverse rule when increasing one decreases the other (more workers = fewer days).
What is the compound rule of three?
It applies when more than two quantities are related to the result. Each quantity can have a direct or inverse relationship with the value being sought.
What is the rule of three used for in everyday life?
For scaling recipes, calculating distances on maps and plans, converting currencies, estimating working times, calculating discounts and solving any proportionality problem.
What is the formula for the direct rule of three?
If A → B and C → X, then X = (C × B) / A. Multiply the extremes and divide by the known term on the same side.