A rule of three calculator online solves any direct proportion problem in seconds - enter three known values and find the missing fourth without pen and paper.
What is the Rule of Three?
The rule of three (also known as cross multiplication or proportional calculation) is a mathematical technique to find an unknown value when three values in a proportion are known.
The structure is: A is to B as C is to X
Solving for X: X = (B × C) / A
This is the "direct" rule of three - when A increases, B increases proportionally. There is also an "inverse" rule of three (when A increases, B decreases), but the direct version covers the vast majority of everyday cases.
How to Use the Rule of Three Calculator
- Open the Rule of Three Calculator on UtilWave.
- Fill in the three known values:
- A and B - the reference pair (e.g., "5 workers" and "10 days")
- C - the new input value (e.g., "8 workers")
- The calculator instantly computes X (e.g., "how many days with 8 workers").
- The relationship used (A/B = C/X) is shown for transparency.
Common Use Cases
Recipe scaling - If 4 servings need 300g of flour, how much flour do 10 servings need?
- A=4, B=300, C=10 → X = 750g
Unit pricing - If 3 liters of paint cover 24 m², how much area does 5 liters cover?
- A=3, B=24, C=5 → X = 40 m²
Speed and time - If a car travels 120 km in 2 hours, how far does it travel in 5 hours?
- A=2, B=120, C=5 → X = 300 km
Currency conversion - If 1 USD = 5.10 BRL, how many BRL is 75 USD?
- A=1, B=5.10, C=75 → X = 382.50 BRL
Construction planning - If 2 workers lay 150 bricks per day, how many bricks can 7 workers lay?
- A=2, B=150, C=7 → X = 525 bricks
Direct vs Inverse Proportion
The tool handles direct proportions (both quantities increase together). For inverse proportions (one increases as the other decreases), the formula changes:
X = (A × B) / C
Example: If 4 workers finish a job in 12 days, how many days do 6 workers need? X = (4 × 12) / 6 = 8 days
FAQ
What is cross multiplication? Cross multiplication is the algebraic technique behind the rule of three. In the proportion A/B = C/X, cross-multiplying gives A × X = B × C, so X = (B × C) / A.
Can I use decimals? Yes - the calculator handles decimal and fractional inputs with the same formula.
What if I need to find A, B, or C instead of X? Rearrange the values so the unknown is always in the X position. Any of the four positions can be solved by placing the other three in the A, B, C fields.
Is this the same as a percentage calculation? Percentage calculations are a special case of the rule of three where one of the reference values is 100. For pure percentage questions, the Percentage Calculator is more convenient.
Solve any proportion in seconds with the free Rule of Three Calculator.