Ratio Calculator
Simplify a ratio to its lowest terms and see the equivalent proportion per unit.
How to use this calculator
- Enter the two sides of the ratio as whole numbers.
- The calculator divides both by their greatest common divisor to reach the simplest form.
The formula
A : B = (A ÷ GCD) : (B ÷ GCD)- GCD
- Greatest common divisor — the largest whole number dividing both A and B
How it works
Two ratios are equivalent when one is a scaling of the other. 24:36 is the same relationship as 2:3 because both sides were divided by 12.
The greatest common divisor is found with the Euclidean algorithm: repeatedly replace the larger number by the remainder of the division until the remainder is zero.
Worked example
A recipe serves 24 people with 36 cups of flour; simplify the ratio.
- 1GCD of 24 and 36 is 12
- 224 ÷ 12 = 2
- 336 ÷ 12 = 3
The simplified ratio is 2:3 — 2 parts people-batches to 3 parts flour.
When this calculator is useful
- Scaling recipes
- Mixing paint, concrete, or fertilizer
- Comparing screen aspect ratios
- Map and model scales
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both sides by 10, 100, etc. until both are whole numbers, then simplify normally.
Is 2:3 the same as 4:6?
Yes — equivalent ratios describe the same proportional relationship, just scaled.