Formula
Direct: A ÷ B = C ÷ D ⇒ A·D = B·CInverse: A × B = C × D
- Leave exactly one of A, B, C, D empty — that is the value to find.
Cross-multiply, then divide by the number opposite the unknown.
Worked examples
2 : 3 = 4 : ?
- Type of proportion
- Direct: A ÷ B = C ÷ D (both rise together)
- A
- 2
- B
- 3
- C
- 4
Missing value (D)
6
6 workers, 10 days → 12 workers
- Type of proportion
- Inverse: A × B = C × D (one rises as the other falls)
- A
- 6
- B
- 10
- C
- 12
Missing value (D)
5
How it works
In a direct proportion, if 2 pens cost 3 then 4 pens cost 6: 2 ÷ 3 = 4 ÷ D, so D = 3 × 4 ÷ 2 = 6. This is the “unitary method” or “rule of three” taught in school.
In an inverse proportion the product stays constant: if 6 workers need 10 days, 12 workers need 6 × 10 ÷ 12 = 5 days. For worked examples with several workers see Time and Work Calculator, and for speed and travel see Speed, Time and Distance Calculator.
To compare quantities as a ratio rather than solve for a missing value use Ratio Calculator.
Assumptions and limits
- Exactly three boxes must be filled in.
- Cases that would need division by zero are rejected with a message naming the box.
Related tools
Ratio CalculatorSimplify a ratio to lowest terms, or split an amount in a given ratio.Percentage CalculatorFind X% of a number, what percent one number is of another, or the whole from a part.Time and Work CalculatorHow long a job takes when several workers share it, or one worker's missing time.Speed, Time and Distance CalculatorFind speed, time or distance when you know the other two, in your choice of units.Fraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers, simplified automatically.Linear Equation SolverSolve ax + b = c, or two equations in x and y, with steps and a check.