To simplify a ratio, divide both sides by their greatest common divisor. So 8:12 becomes 2:3, because 4 divides into both. The ratio calculator does this for you, including the case where the numbers are decimals.
Here is the method in full.
The basic method
A ratio compares two quantities, and like a fraction it can be written in many equivalent forms. 8:12, 4:6 and 2:3 all describe the same relationship. The simplest form uses the smallest whole numbers, which you get by dividing both sides by their greatest common divisor.
For 8:12, the greatest common divisor is 4. Dividing both sides gives 8 ÷ 4 : 12 ÷ 4, which is 2:3. That is the ratio in lowest terms, because 2 and 3 share no common factor above 1.
Finding the greatest common divisor
The greatest common divisor is the largest number that divides both sides exactly. For small numbers you can often see it, but for larger ones the reliable way is Euclid’s method, covered in how to find LCM and GCD. The ratio calculator finds it for you, so you only enter the two numbers.
Ratios with decimals
If a ratio has decimals, scale both sides up to whole numbers first, then simplify. For 0.5:0.25, multiply both by 100 to get 50:25, whose greatest common divisor is 25, giving 2:1. The rule is to multiply by the same power of ten on both sides so the relationship stays the same.
Solving a proportion
A proportion says two ratios are equal, like 2:3 = 10:?. To find the missing value, cross-multiply: the missing term is B × C ÷ A. Here that is 3 × 10 ÷ 2 = 15, so 2:3 = 10:15. This is how map scales and recipe scaling work. Enter the three known numbers in the solve mode of the calculator and it fills in the fourth.
Where this comes up
Ratios appear wherever two quantities need to stay in proportion:
- Recipes and mixes, such as a 2:1 ratio of flour to water scaled up to a batch.
- Maps and models, where a scale like 1:50 links a model measurement to the real one.
- Sharing, where a simplified ratio shows the cleanest way to split an amount.
To compare two quantities as a single percent instead, see how to calculate a percentage, or open the ratio calculator to try it now.