Ratio Calculator
Simplify ratios to their lowest terms, solve missing values in proportions, and scale ratios up or down.
Simplify a ratio
Simplified Ratio
Solve a proportion — find the missing value
Missing Value
Scale a ratio
Scaled Ratio
Are two ratios equivalent?
Result
How to Work with Ratios
A ratio expresses the relationship between two quantities. Ratios appear everywhere — ingredient proportions in recipes, map scales, currency exchange rates, and aspect ratios on screens.
Simplifying a Ratio
Find the Greatest Common Divisor (GCD) of both numbers and divide each by it.
Example: 18:12 → GCD(18,12) = 6 → 3:2.
Solving Proportions
If A:B = C:D, then A × D = B × C (cross-multiplication).
To find D: D = (B × C) / A
Example: 2:3 = 10:? → D = (3 × 10) / 2 = 15.
Scaling a Ratio
Multiply both parts by the same factor. Scaling 3:2 by 5 gives 15:10, which still simplifies to 3:2.
Frequently Asked Questions
A ratio compares two quantities. The ratio 3:2 means "3 for every 2". Ratios can represent fractions, scales, recipes, speeds, and many real-world relationships.
Divide both numbers by their Greatest Common Divisor (GCD). For example, 12:8 → GCD is 4 → divide both by 4 → 3:2.
A proportion states that two ratios are equal: A:B = C:D. If three values are known, the fourth can be found with cross-multiplication: D = (B × C) / A.
Multiply both parts of the ratio by the same number. Scaling 3:2 by 4 gives 12:8. This is useful for recipes, maps, and scale models.
Yes. Both simplify to 2:3. Two ratios are equivalent if they reduce to the same simplified form.