Simplify a ratio
Enter two whole numbers or decimals to reduce their ratio to its simplest form.
Check equivalent ratios
Find out whether two ratios represent the same proportion.
Find a missing value
Enter three values in A : B = C : D. Leave the value you want to solve blank.
What is a ratio?
A ratio compares the relative size of two or more quantities. The ratio 2:3 is read as “2 to 3” and means that for every 2 of the first quantity, there are 3 of the second.
How to simplify a ratio
Divide every term by its greatest common factor. For example, 12:18 can be divided by 6, giving the simplified ratio 2:3. Ratios can also be scaled up or down by multiplying or dividing every term by the same number.
How equivalent ratios work
Equivalent ratios show the same relationship using different numbers. For example, 2:3 and 4:6 are equivalent because both terms in the first ratio have been multiplied by 2.
Finding a missing ratio value
If three values in a proportion are known, you can find the fourth by keeping the ratio equivalent. For example, 2:3 = 4:D, so D = 4 × 3 ÷ 2 = 6.
Ratio examples in everyday life
Ratios are useful when scaling recipes, mixing paint or concrete, comparing ingredients, sharing costs or converting map scales. A 1:2:3 mix means one part of the first material, two parts of the second and three parts of the third.
Separate a part-to-part ratio from a share of the total
For a 3:5 mixture, there are eight parts altogether. In a total of 40 units, the shares are 15 and 25. The first share is 3/8 of the mixture, not 3/5. Label both quantities before scaling so that reversing their order does not change the intended recipe or allocation.
Frequently asked questions
Is 2:3 the same as saying two thirds of the total?
No. In a two-part split of 2:3, the first share is 2 out of 5 total parts. The fraction 2/3 compares the first quantity with the second.
How do I simplify 18:30?
Divide both terms by their greatest common factor, 6, to get 3:5.
Does the order of a ratio matter?
Yes. If red to blue is 2:3, blue to red is 3:2. Keep the labels in the same order when comparing ratios.
How do I split 40 in a ratio of 3:5?
There are eight parts, each worth 5. The shares are 15 and 25.
Should I convert units before simplifying?
Yes when comparing the same kind of measurement. For example, 1 m to 50 cm becomes 100 cm to 50 cm, or 2:1.
How can I check equivalent ratios?
For nonzero second terms, compare cross products: A:B and C:D are equivalent when A × D equals B × C.