Ratio Calculator

Ratio calculator at a glance#

A ratio calculator simplifies a ratio to its lowest terms and solves for a missing value in a proportion. A ratio such as 2:3 compares two quantities, meaning 2 units of the first for every 3 units of the second. The same ratio can be written as the fraction 2/3 or read as "2 to 3."

How do you simplify a ratio?#

To simplify a ratio, divide both parts by their greatest common factor (GCF). For 8:12, the GCF of 8 and 12 is 4, so divide both by 4 to get 2:3. The ratio 2:3 is the simplest form because 2 and 3 share no factor larger than 1.

How do you solve a proportion with a missing value?#

When two ratios are equal, cross multiply to find the unknown. For 1:2 = x:10, multiply 1 by 10 to get 10, then divide by 2, so x is 5. Check it: 1:2 and 5:10 both simplify to 1:2, so they match.

Enter your ratio or proportion in the calculator above for the simplified result and any missing value. Ratios show relative size, not totals, so a recipe scaled to 2:3 keeps the same proportion at any batch size.

Types of ratios#

A simple ratio compares two quantities directly, like 4 red marbles to 6 blue, written 4:6 or simplified to 2:3. A compound ratio compares three or more parts at once, such as 2 parts flour to 1 part sugar to 1 part butter, written 2:1:1. A rate compares two different units, such as miles per hour or dollars per gallon, and is usually left in that form rather than reduced.

Part-to-part vs part-to-whole#

A part-to-part ratio compares one group to another, so 4 red to 6 blue marbles is 4:6. A part-to-whole ratio compares one group to the total. With 4 red and 6 blue, the whole is 10, so red-to-total is 4:10, which simplifies to 2:5 and equals 40%. Add the parts of a ratio to convert it to a fraction or percentage of the whole.

Equivalent ratios#

Two ratios are equivalent when both parts are multiplied or divided by the same nonzero number. Starting from 2:3, multiply both parts by 4 to get 8:12, which is the same relationship at a larger scale. This is why you can scale a recipe up or down without changing how it tastes: the proportion stays fixed.

Ratio FAQ#

How do you write a ratio in three different ways?#

A ratio of 2 to 3 can be written with a colon as 2:3, as the fraction 2/3, or in words as "2 to 3." All three mean 2 units of the first quantity for every 3 of the second.

How do you calculate equivalent ratios?#

Multiply or divide both parts by the same nonzero number. From 2:3, multiplying both parts by 5 gives 10:15, and dividing 10:15 by 5 returns 2:3. The relationship between the two quantities does not change.

What is the simplest form of a ratio?#

A ratio is in simplest form when its two parts share no common factor other than 1. For 6:9, the GCF is 3, so it reduces to 2:3, and 2 and 3 cannot be reduced further.

How do ratios solve scaling problems?#

Set the known ratio equal to the scaled one and cross multiply. To triple a 2:3 mix, solve 2:3 = x:9: multiply 3 by the scale to reach 9, so x is 6, giving 6:9. The calculator above does this for any missing value.