The formula
How it works
A ratio compares two quantities. Enter a known ratio A : B and one term C of an equal ratio, and the calculator solves for the missing term D — then shows the ratio in its simplest whole-number form.
FAQ
How do I simplify a ratio?
Divide both sides by their greatest common factor. For example 8 : 12 both divide by 4, giving 2 : 3. The calculator does this automatically for whole-number ratios.
What is a proportion?
A proportion is a statement that two ratios are equal, like 2 : 3 = 10 : 15. Solving one is called “cross-multiplying”, because A × D equals B × C.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities, like 2 boys to 3 girls, while a fraction usually expresses a part out of a whole, like 2 out of 5 students. They use the same arithmetic, but a ratio’s two numbers do not have to add up to a total.
How do I work with a ratio that has three terms, like A : B : C?
Treat it the same way — divide all three parts by their greatest common factor to simplify, or scale all three by the same multiplier to find an equivalent ratio. This calculator handles two-term ratios; for three terms, apply the same scaling factor to every part by hand.
How do I scale a ratio up or down, like for a recipe?
Multiply every part of the ratio by the same number. If a recipe uses flour to sugar in a 2 : 1 ratio and you want to double it, both parts double to 4 : 2, which is still the same ratio.
Is a ratio the same as a percentage?
Not quite — a ratio compares two quantities directly, while a percentage expresses one quantity as a fraction of 100. You can convert a ratio to a percentage by turning it into a fraction of the total and multiplying by 100.
Does the order of the terms in a ratio matter?
Yes. A ratio of 2 : 3 is not the same as 3 : 2 — the first number always corresponds to the first quantity you are comparing, so swapping the order changes what the ratio means.
About the ratio calculator
This calculator solves ratio problems and simplifies ratios to their lowest terms. A ratio is a way of comparing two amounts — how many of one thing there are for each of another — and it turns up whenever you scale a recipe, mix a solution, or read a map. The calculator handles the two most common tasks: finding a missing value in a proportion, and reducing a ratio to its simplest form.
How to use it
Enter the two parts of your known ratio as A and B, then enter C, the first part of an equivalent ratio. The calculator finds D, the value that makes A : B equal to C : D. For example, with the ratio 2 : 3, scaling up so the first part is 10 gives a second part of 15, because 2 : 3 = 10 : 15. It also shows your original ratio simplified — 8 : 12 would be reduced to 2 : 3 — so you can see the cleanest form.
The formula
Equal ratios form a proportion, . Cross-multiplying gives , which rearranges to solve for the missing term: . To simplify a ratio, divide both parts by their greatest common factor, . Because a ratio and a fraction are really the same idea written differently, every rule for fractions applies to ratios too.
Where it is used
Ratios are everywhere in daily life and work. Cooks scale recipes up or down while keeping ingredients in proportion, and builders mix concrete or mortar to a set ratio of cement to sand. Map scales, model kits and blueprints all use ratios, as do aspect ratios for screens and photos. In business, financial ratios compare figures like debt to income, and in chemistry ratios set how much of each substance goes into a reaction.