Ratio Calculator — simplify a ratio to lowest terms

How it works

A ratio a : b compares two quantities — how much of one there is for each amount of the other. Like a fraction, a ratio can be written in many equivalent forms (18 : 24, 9 : 12 and 3 : 4 all say the same thing), and the simplest form is the one whose terms share no common factor.

To get there, divide both terms by their greatest common divisor — the largest whole number that divides both exactly:

simplified ratio = a ÷ gcd(a, b) : b ÷ gcd(a, b)

A ratio is also just a division in disguise: a : b equals the quotient a ÷ b, which is its decimal value. That's handy for comparing ratios — 3 : 4 = 0.75 and 5 : 8 = 0.625, so 3 : 4 is the larger ratio.

Worked example

Simplify 18 : 24. The greatest common divisor of 18 and 24 is 6, so divide both terms by 6:

18 : 24 = (18 ÷ 6) : (24 ÷ 6) = 3 : 4

As a decimal that's 18 ÷ 24 = 0.75. Another example: a 1920 : 1080 screen has a GCD of 120, simplifying to 16 : 9 — the widescreen aspect ratio — with a decimal of about 1.78.

Frequently asked questions

How do I simplify a ratio?

Find the greatest common divisor of the two terms and divide both by it. For 20 : 30, the GCD is 10, giving 2 : 3. If you can't spot the GCD at once, divide by any common factor you notice and repeat — 20 : 30 → 2 : 3 also works by dividing by 10 in two steps of 2 then 5.

What is the greatest common divisor?

The largest whole number that divides both terms without a remainder. For 18 and 24 it's 6; for 16 and 9 it's 1 (they share no factor, so 16 : 9 is already in lowest terms). Dividing by the GCD in one go lands you directly at the simplest form.

What's the difference between a ratio and a fraction?

They're closely related — both compare a to b — and a ratio a : b has the same value as the fraction a/b. The difference is mostly in use: a fraction usually names a part of a whole (3/4 of a pizza), while a ratio compares two separate quantities (3 parts water to 4 parts flour). The arithmetic of simplifying is identical.

How do I turn a ratio into a decimal or percentage?

Divide the first term by the second — that's the decimal (3 : 4 = 0.75). Multiply by 100 for a percentage (75%). This is why a ratio and its quotient are interchangeable: the colon is just another way of writing a division.

Can a ratio have more than two terms?

Yes — ratios like 2 : 3 : 5 compare three or more quantities, and you simplify them the same way, dividing every term by the GCD of all of them. This calculator handles the common two-term case; for three-part ratios, reduce them by the overall greatest common divisor by hand.

Does the order of the terms matter?

Yes. 3 : 4 and 4 : 3 are different ratios — the first says three of something for every four of another, the second reverses it. Keep the terms in the order the problem states them; swapping them inverts the relationship (and the decimal becomes its reciprocal, 0.75 versus about 1.33).