Ratio Calculator
Simplify any two-number ratio to its lowest terms and explore equivalent ratios in seconds. Ideal for cooking, map scaling, financial analysis, and mixing solutions where proportional relationships matter.
About this calculator
A ratio expresses the relative size of two quantities and is written as a : b or as the fraction a / b. To simplify a ratio, divide both values by their greatest common divisor (GCD) — the largest integer that divides both a and b without a remainder. For example, 12 : 8 simplifies to 3 : 2 because GCD(12, 8) = 4. The simplified form preserves the proportional relationship while using the smallest whole numbers. Equivalent ratios are obtained by multiplying or dividing both terms by the same non-zero number. Ratios appear in recipes, maps, scale models, financial statements, and probability calculations.
How to use
Enter a = 18 and b = 24. The calculator computes a / b = 18 / 24 = 0.75, and finds GCD(18, 24) = 6, giving the simplified ratio 3 : 4. This means for every 3 units of the first quantity there are 4 units of the second. To find an equivalent ratio scaled up by 5, simply multiply both terms: 15 : 20. The decimal value 0.75 also confirms that the first quantity is 75% the size of the second.
Frequently asked questions
What is the difference between a ratio and a fraction?
A fraction represents a part of a whole — numerator divided by denominator — while a ratio compares two separate quantities that may or may not be parts of the same whole. For instance, 3/4 as a fraction means 3 out of 4 equal parts, but 3 : 4 as a ratio could compare 3 apples to 4 oranges. Mathematically both are computed the same way, but ratios can compare any two related quantities, not just a part to its whole.
How do I simplify a ratio to its lowest terms manually?
Find the greatest common divisor (GCD) of both numbers using the Euclidean algorithm: repeatedly subtract the smaller number from the larger until both are equal — that value is the GCD. Then divide each term of the ratio by the GCD. For example, to simplify 36 : 48, compute GCD(36, 48) = 12, then 36/12 = 3 and 48/12 = 4, giving 3 : 4. Always verify by checking that 3 and 4 share no common factor other than 1.
When should I use a ratio instead of a percentage to compare quantities?
Ratios are preferable when you want to preserve the individual scale of both quantities rather than express one as a fraction of a total. In recipes, for instance, a ratio of 2 : 3 flour to sugar clearly shows the absolute relationship regardless of batch size. Percentages collapse both numbers into a single value relative to 100, which can obscure how much of each ingredient you actually need. For mixing, scaling, or comparing two independent measures, ratios give clearer, more actionable information.