What is a ratio?
A ratio compares the sizes of two quantities. A statement of 12:18 indicates that for every 12 units of the first quantity, there are 18 units of the second. If both quantities have the same units, the ratio can be simplified without changing its meaning.
Simplify with the greatest common divisor
Find the greatest common divisor (GCD) of the two terms, then divide both terms by that value.
Simplified ratio = (first ÷ GCD) : (second ÷ GCD)
For 12:18, the GCD is 6, so the simplest ratio is 2:3.
Calculate an equivalent ratio
Multiply both terms by the same positive whole number. Scaling 2:3 by 2 gives 4:6, and scaling by 5 gives 10:15. All three ratios express the same relationship.
Order matters
A recipe that calls for flour to water in a 3:2 ratio is not the same as 2:3. Write the terms in the correct order and make sure the quantities use compatible units before comparing them.
Using ratios in everyday problems
Ratios help scale cooking ingredients, interpret maps, compare groups, and check proportions in design. If you need to find a missing fourth number in two equivalent ratios, use the Proportion Calculator.
Inputs and limitations
This calculator uses positive integers. Negative values, zero terms and decimals are excluded, and very large integer inputs are rejected to keep calculations predictable. For fractions or decimals, convert the amounts to suitable integer quantities first.
Learn the method step by step
Read how to simplify ratios for worked examples and common ratio mistakes.