Ratio
→ Use the Ratio CalculatorWhat is Ratio?
A ratio expresses the relative sizes of two or more quantities of the same kind. Written as a:b or $$\frac{a}{b}$$, it answers the question "how many times larger is one quantity than another?" A ratio of 3:1 means the first quantity is three times the second. The two quantities must share the same unit for the ratio to be dimensionless — mixing kilograms and metres produces a rate, not a ratio.
A ratio does not carry information about absolute magnitudes — only proportions. A 3:1 ratio describes a recipe with 3 cups flour to 1 cup sugar, a business with 3 assets for every 1 unit of liability, or a sample with 3 red marbles to 1 blue marble. The underlying scale is irrelevant to the ratio itself.
Ratios are expressed in simplest form by dividing both terms by their greatest common divisor. The ratio 12:8 simplifies to 3:2. When more than two quantities are compared, extended ratios (a:b:c) are used — a concrete mix of 1:2:4 (cement:sand:gravel) retains the same interpretation: proportional relationships among all listed quantities.
When to use Ratio
Use ratios when comparing the relative sizes of two or more same-unit quantities and the proportion is what matters, not the absolute values. Use a fraction when expressing a part-to-whole relationship. Use a rate when the quantities have different units (e.g., distance per time). Use a percentage when communicating a proportion to a general audience.
Worked examples
| Context | Ratio | Interpretation |
|---|---|---|
| Debt-to-equity | 2:1 | Two dollars of debt for every dollar of equity |
| Map scale | 1:50,000 | 1 cm on map = 50,000 cm (500 m) in reality |
| Recipe (flour:sugar) | 3:1 | Three parts flour to one part sugar |
| Screen aspect ratio | 16:9 | Width is 16/9 times the height |
| Gear ratio | 4:1 | Input shaft rotates 4 times per output rotation |
Common pitfalls
Order is not interchangeable. A debt-to-equity ratio of 3:1 is not the same as 1:3. Always state which quantity comes first, and be consistent. When a ratio is written as a single fraction (e.g., 0.75 for a 3:4 ratio), the implied denominator is 1, making it a unit rate — a different concept from the original two-part ratio.
Frequently asked questions
How is a ratio different from a fraction?
A fraction represents a part of a whole: the denominator is the total. A ratio compares two separate quantities: neither term is necessarily the total. In a class with 12 boys and 8 girls, the boy-to-girl ratio is 12:8 (simplified to 3:2), while the fraction of boys in the class is 12/20 = 3/5.
How do I simplify a ratio?
Divide both terms by their greatest common divisor (GCD). For 18:24, the GCD is 6, giving a simplified ratio of 3:4. For multi-term ratios, divide all terms by the GCD of the entire set. The ratio 6:9:15 has a GCD of 3, simplifying to 2:3:5.
Can a ratio have more than two terms?
Yes. An extended ratio compares three or more quantities simultaneously — for example, a paint formula expressed as red:blue:yellow = 2:3:1. The same proportion rules apply: all terms scale together, and simplification uses the GCD of all terms.