How to simplify a ratio
A ratio compares two quantities, written a:b. To simplify it, divide both numbers by their greatest common divisor (GCD), the largest number that divides both exactly. The ratio 12:18 has a GCD of 6, so it simplifies to 2:3.
The simplified ratio is equivalent to the original: for every 2 of the first quantity there are 3 of the second.
Turning a ratio into fractions and percentages
A ratio a:b splits a total into a + b equal parts. In 2:3 there are 5 parts, so the first quantity is 2/5 (40%) of the total and the second is 3/5 (60%).
Ratios with decimals
This calculator works with whole numbers. If your ratio has decimals, multiply both numbers by 10 (or 100) until they are whole. For example, 1.5:4.5 becomes 15:45, which simplifies to 1:3.
Worked examples
12 : 18
= 2:3
The GCD of 12 and 18 is 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
45 : 30
= 3:2
The GCD is 15: 45 ÷ 15 = 3 and 30 ÷ 15 = 2.
8 : 20
= 2:5
The GCD is 4: 8 ÷ 4 = 2 and 20 ÷ 4 = 5.
100 : 75
= 4:3
The GCD is 25: 100 ÷ 25 = 4 and 75 ÷ 25 = 3.
Frequently asked questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor. For 12:18 the GCD is 6, so the ratio simplifies to 2:3.
Does the order of a ratio matter?
Yes. 2:3 and 3:2 are different ratios: the first compares the first quantity to the second, and the second does the opposite.
How do I use a ratio to share an amount?
Add the parts, divide the total by that sum, then multiply by each part. To share 50 in the ratio 2:3, there are 5 parts, each worth 10, so the shares are 20 and 30.
What if the ratio is already in simplest form?
Then the GCD is 1 and the calculator returns the same numbers. For example, 7:9 stays 7:9.
Can I enter decimals?
Not directly. Multiply both numbers by 10 or 100 until they are whole numbers, then simplify.