Ratio calculator

Reduce a ratio to its simplest whole numbers or scale it up and down.

Formula Maths

Simplest form

As 1 : n, n is: ≈ 1.3333
A ÷ B: 0.75

A15

B20

Step by step

15 : 20
= 3 : 4 (÷ 5)

How it works

To simplify, the calculator first turns any decimals into whole numbers by multiplying both sides by the same power of ten. It then divides both by their greatest common divisor.

To scale, it keeps the ratio equal: if A : B = C : x, then x = B × C ÷ A.

Formula

A : B = (A ÷ g) : (B ÷ g), g = gcd(A, B)
A : B = C : x → x = B × C ÷ A

Worked example

15 : 20 has a greatest common divisor of 5, so it simplifies to 3 : 4. Scaling 15 : 20 = 6 : x gives x = 20 × 6 ÷ 15 = 8.

Questions people ask

How do I simplify a ratio with decimals?

Multiply both parts by 10, 100 or more until they are whole numbers, then divide by their greatest common divisor. 1.5 : 2 becomes 15 : 20, then 3 : 4.

What does a ratio of 1 : n mean?

It says how many of B there are for each single A. 3 : 4 is 1 : 1.333…

Is a ratio the same as a fraction?

They are closely related: the ratio 3 : 4 means A is 3/4 of B. But a ratio compares two parts, while a fraction usually compares a part with a whole.