Ratio Calculator

How Ratio Simplification Works

A ratio A : B is reduced to lowest terms by dividing both A and B by their greatest common factor (GCF), the largest number that divides both evenly. This calculator finds the GCF using the Euclidean algorithm — repeatedly replacing the larger number with the remainder of dividing it by the smaller number until the remainder reaches zero — which is exact for any pair of integers, no matter how large. If either input isn't a whole number, both sides are first scaled up by a power of 10 so the ratio reduces cleanly, then still expressed in lowest integer terms.

Ratio, Fraction, and Percentage Are the Same Relationship

A ratio of A : B carries the same information as the fraction A/B and the decimal A ÷ B — they're just different notations for comparing two quantities. Expressing each part as a percentage of the whole (A + B) is useful for splitting a total in a given ratio, such as dividing a bill, a mix, or a budget between two parties. For working with the fraction form directly, see the fraction calculator; to convert the result to a percentage of a different base, try the percentage calculator.

A Common Mix-Up: Ratio vs. Rate

A ratio compares two quantities of the same kind (4 apples : 8 apples simplifies to 1 : 2), while a rate compares two different kinds of quantities (miles per hour, price per item) and generally isn't "simplified" the same way. Also note that simplifying a ratio doesn't change what it represents — 1 : 2 and 4 : 8 describe the exact same proportion, just as 1/2 and 4/8 are the same fraction.