A ratio compares two quantities, and simplifying it to lowest terms makes the relationship easier to understand at a glance — similar to reducing a fraction. This calculator simplifies any two positive numbers to their simplest whole-number ratio.
The formula
Where gcd is the greatest common divisor. For 8 and 12, the greatest common divisor is 4, so 8 ÷ 4 : 12 ÷ 4 simplifies to 2 : 3.
Worked examples
| Original ratio | Simplified |
|---|---|
| 10 : 15 | 2 : 3 |
| 25 : 100 | 1 : 4 |
| 9 : 6 | 3 : 2 |
Common uses
- Recipe scaling: keeping ingredient ratios consistent when doubling or halving a recipe.
- Aspect ratios: understanding and comparing screen or image proportions.
- Mixing ratios: paint, concrete, or chemical mixtures often specified as simplified ratios.
- Maps and scale models: expressing scale as a simplified ratio like 1:100.
Common mistakes
- Confusing ratio with fraction notation. A ratio of 2:3 is related to but not identical in meaning to the fraction 2/3 — a ratio compares two separate quantities, while a fraction represents a part of a whole.
- Not fully reducing. Stopping at a common factor that isn't the greatest common divisor leaves the ratio not fully simplified.
Frequently asked questions
How do I simplify a ratio?
Find the greatest common divisor of both numbers and divide each side of the ratio by it.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (like 2 cups flour to 3 cups sugar), while a fraction represents a part of a single whole. They're related but not always interchangeable.
Can this calculator handle decimal inputs?
Yes, though ratios are most commonly expressed and simplified using whole numbers; the calculator will still find the simplified relationship for decimal inputs.