Ratio calculator
Three tools for ratios: put a ratio in lowest terms, find the missing number of a proportion, or share an amount in the ratio of its parts. Fill in the boxes of the one you need.
Simplify a ratio
This answer is for the example values in the boxes above. 12 : 18. Change the boxes to see your own answer.
Find the missing number of a proportion
Share an amount in a ratio
How it works
The first tool finds the greatest common factor of the numbers and divides each of them by it. When a number has decimals, it first multiplies all of them by 10, 100 and so on, up to six decimals, until each is whole. It also writes each number as a fraction of the whole and as a percent.
The second tool uses the rule that in a proportion A : B = C : D, the cross products A × D and B × C are equal. Choose which of the four numbers to find and fill in the other three. The tool multiplies the two on the other diagonal and divides by the one opposite.
The third tool adds the parts of the ratio, divides the amount by that sum and multiplies by each part.
A worked example
The ratio 12 : 18 has the greatest common factor 6, so in lowest terms it is 2 : 3. The whole is 5 parts, so the two numbers are 2/5 and 3/5 of it, which is 40 percent and 60 percent.
In 2 : 3 = 8 : D, the missing D is 3 × 8 ÷ 2, which is 12. The check is 2 × 12 = 3 × 8, with 24 on both sides. In 7 : 3 = 5 : D the answer is 15/7, shown as 2.142857, rounded to six decimals.
An amount of 1,000 shared in the ratio 2 : 3 : 5 is 200, 300 and 500. The parts add up to 10, so each part is worth 100.
Decimals and zeros
A number may have up to six decimals, and a seventh is rounded away. The ratio 0.5 : 0.25 is multiplied by 100 to give 50 : 25, and divided by 25 to give 2 : 1. The first tool accepts a 0, so 0 : 5 is 0 : 1. In a proportion the three numbers that you know must be above 0, and an answer too large to show is refused.
What it leaves out
The first tool takes two or three numbers, and the third shares an amount among up to four parts. A ratio of two different units, such as feet to inches, has to be put in the same unit first. The shares are rounded to two decimals.
Questions
How do I simplify a ratio?
Divide every number by their greatest common factor. For 12 : 18 the factor is 6, so the ratio is 2 : 3. For 8 : 12 : 20 the factor is 4, which gives 2 : 3 : 5.
How do I simplify a ratio with decimals?
Multiply every number by 10, 100 or another power of 10 until none has a decimal, then divide by the greatest common factor. 1.5 : 2.5 becomes 15 : 25, and then 3 : 5.
How do I solve a proportion?
Cross-multiply. In A : B = C : D the products A × D and B × C are equal, so D is B × C ÷ A. For 2 : 3 = 8 : D, D is 3 × 8 ÷ 2, which is 12.
How do I turn a ratio into fractions and percents?
Add the numbers to get the whole, and put each number over it. The ratio 2 : 3 makes the fractions 2/5 and 3/5, which are 40% and 60%.
How do I share an amount in a ratio?
Divide the amount by the sum of the parts and multiply by each part. 1,000 in the ratio 2 : 3 : 5 is 200, 300 and 500.
Why do the shares not always add up to the amount?
Each share is rounded to two decimals. 0.01 shared in the ratio 1 : 1 is 0.005 each, which rounds to 0.01, so the shares add up to 0.02. The calculator says so under the answer.
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