Ratio Calculator
Simplify a ratio to its lowest terms, and find an equivalent value for a scaled ratio.
How this calculator works
A ratio is simplified by dividing both terms by their greatest common divisor. A scaled equivalent ratio keeps the same proportion between terms.
gcd = greatest common divisor of A and B
Ratios in everyday contexts
Ratios show up constantly in practical situations: scaling a recipe up or down while keeping ingredient proportions consistent, mixing paint or chemicals in the correct proportion, or converting a map scale to real-world distances.
Simplifying a ratio to its lowest terms (like reducing 12:18 to 2:3) makes it easier to understand and compare to other ratios, similar to how simplifying a fraction makes it easier to work with.
A worked example
The ratio 24:36 simplifies to 2:3 (dividing both by their greatest common divisor, 12). If you wanted to scale so the first term becomes 10, the second term would need to become 15 to preserve the same 2:3 ratio.
This is exactly how recipe scaling works — if a sauce recipe calls for a 24:36 (2:3) ratio of vinegar to oil in milliliters, scaling the vinegar to 10ml means using 15ml of oil to keep the same flavor balance.
Ratios in everyday scaling problems
Ratios show up constantly in scaling problems — adjusting a recipe for a different number of servings, resizing an image while keeping proportions, mixing paint or chemical solutions in the right proportion, and converting between map scale and real-world distance all rely on the same equivalent-ratio logic this calculator uses.
A ratio simplified to its lowest terms (like 12:18 simplified to 2:3) represents the same proportional relationship as the original — simplifying just makes the relationship easier to see and work with.
Frequently asked questions
What does the 'scaled' value show?
It shows what B would need to be to keep the same ratio if A were scaled to the value you entered in the 'If A becomes' field.
How do I scale a recipe using ratios?
Keep the ratio between ingredients constant — if a recipe calls for a 2:1 ratio of flour to sugar and you want to double it, use 4:2 (which simplifies back to the same 2:1 ratio) to maintain the same taste and texture.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (like 3 apples to 5 oranges), while a fraction typically represents a part of a single whole — though ratios can be expressed in fraction form for calculation purposes.
Is a simplified ratio the same as the original?
Yes — simplifying a ratio to lowest terms doesn't change the proportional relationship it represents, it just expresses it with smaller numbers.