Ratio Calculator
Enter a ratio to simplify it to lowest terms, and optionally enter a third number to solve a proportion — finding the missing fourth value that keeps the ratio equivalent.
How the Ratio formula works
Simplifying uses the greatest common divisor (GCD):
Simplified ratio = (A / GCD(A,B)) : (B / GCD(A,B))
Solving a proportion A:B = C:D for the missing value:
D = (B × C) / A
Step-by-step calculation
- Find the greatest common divisor of the two ratio terms.
- Divide both terms by that GCD to simplify the ratio.
- To solve a proportion, cross-multiply: the missing value equals the product of the two 'inner' or 'outer' known terms divided by the remaining known term.
Worked example
Simplify 18:24 — GCD(18,24) = 6, so the simplified ratio is 3:4. Solving the proportion 3:4 = 12:D gives D = (4 × 12) / 3 = 16.
Frequently asked questions
What's the difference between a ratio and a fraction?
A ratio compares two quantities directly (3:4), while a fraction represents a part of a whole (3/4). They use the same underlying math, but a ratio doesn't necessarily imply 'out of a total' the way a fraction does.
Can ratios have more than two terms?
Yes — ratios like 2:3:5 compare three or more quantities. This calculator handles two-term ratios; for multi-term ratios, simplify by dividing all terms by their shared greatest common divisor.