Ratio Calculator
Simplify ratios, solve proportions, and scale ratios by any factor.
Simplify ratio a : b by dividing by the GCD
About Ratio Calculations
A ratio expresses the relative sizes of two or more quantities. For example, a ratio of 2:3 means for every 2 units of one quantity, there are 3 units of another. Ratios are simplified by dividing both terms by their greatest common divisor (GCD), which is the largest number that divides both values without a remainder.
Solving proportions — finding the missing value when two ratios are equal — uses cross-multiplication. If a:b = c:?, then ? = (b×c)/a. This is a fundamental technique in recipe scaling, map reading, currency conversion, and unit conversion. The proportion is a statement of equal ratios.
Scaling a ratio means multiplying both terms by the same factor, which preserves the ratio's value while changing the actual quantities. This is used in scale models (1:100 scale maps), diluting solutions in chemistry, resizing recipes, and creating proportional drawings. The key property is that two ratios a:b and (k×a):(k×b) are equivalent for any non-zero k.
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