Ratio Calculator
A ratio compares two quantities. This reduces any ratio to its simplest whole-number form, and — if you give it a third number — solves the proportion to find the missing fourth. Handy for recipes, scale drawings, mixing and maps.
Your numbers
Result
- As a decimal (A ÷ B)
- 0.67
- As a percentage
- 66.67%
| Form | Value |
|---|---|
| Simplified ratio | 2:3 |
| As a fraction | 2/3 |
| As a decimal | 0.6667 |
| As a percentage | 66.67% |
Simplifying a ratio
To reduce a ratio, divide both sides by their greatest common divisor. For 8:12 the GCD is 4, so it simplifies to 2:3 — the same relationship in the smallest whole numbers. That is exactly how you reduce a fraction, because a ratio A:B and the fraction A/B carry the same information.
Solving a proportion
A proportion says two ratios are equal: A:B = C:D. If you know three of the four, cross-multiplying finds the last: D = B × C ÷ A. So 8:12 = 20:? gives 12 × 20 ÷ 8 = 30. Enter a value in the Scale A to field to solve it — useful for scaling a recipe, enlarging a drawing, or converting a map distance.
Ratio, fraction, decimal, percent
The same comparison wears several outfits. 2:3 is the fraction 2/3, the decimal 0.667, and about 66.7%. Ratios usually compare parts to parts (2 parts water to 3 parts cement), while a fraction or percent compares a part to the whole. Keep track of which one a problem is really asking for.
Frequently asked questions
Sources
- Euclidean algorithm for the greatest common divisor
- Cross-multiplication for solving proportions