Ratio Calculator
Reduce a ratio to its simplest whole-number form, or find the missing term in a proportion — handy for recipes, maps, mixing and scaling.
Result
Enter your values and select Calculate to see the result.
How to use this calculator
- Simplify a ratio: enter two whole numbers. The calculator divides both by their greatest common divisor.
- Solve a proportion: fill in three of A, B, C and D and leave the unknown box empty.
Formula
To simplify A : B, divide both terms by their greatest common divisor (GCD).
A proportion A : B = C : D means A ÷ B = C ÷ D, so A × D = B × C (cross-multiplication). Solving for each unknown:
- A = B × C ÷ D
- B = A × D ÷ C
- C = A × D ÷ B
- D = B × C ÷ A
Worked example
Simplify 24 : 36
The GCD of 24 and 36 is 12. 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 24 : 36 = 2 : 3.
Scale a recipe
A recipe uses 3 cups of flour for 4 servings. For 20 servings: 3 : 4 = C : 20, so C = 3 × 20 ÷ 4 = 15 cups.
Assumptions and limitations
- Simplifying needs non-negative whole numbers, and at least one term must be greater than zero.
- In a proportion, B and D are the second terms and cannot be zero.
- Proportions accept decimals.
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both terms by the same power of 10 to remove the decimals, then simplify. For example 1.5 : 2 becomes 15 : 20, which simplifies to 3 : 4.
How is a ratio different from a fraction?
A ratio compares two parts (2 : 3), while a fraction compares a part to a whole. In a 2 : 3 mix, the first part is 2/5 of the total.