Ratio Calculator

How it works

A ratio a:b compares two quantities. Multiplying or dividing both terms by the same number does not change it, so 1920:1080, 32:18 and 16:9 are all the same ratio. The simplest form divides both terms by their greatest common divisor; if either term has decimals, both are first multiplied by a power of ten to make them whole numbers.

The same ratio can be read as the fraction a/b, the decimal a ÷ b, and a as a percent of b. Each term's share of the whole is its part of a + b, which is what you use to split a quantity in a given ratio: a total T gives a ÷ (a + b) × T to the first part and b ÷ (a + b) × T to the second.

Scaling to a new first term keeps the ratio and changes the size: the new second term is new a × b ÷ a. Comparing two ratios reduces both to simplest form; they are equal when the simplest forms match, and otherwise the one with the larger a ÷ b is the larger ratio. For screen aspect ratios that means the wider shape.

Formula

simplest form: (a ÷ g) : (b ÷ g),  g = gcd(a, b)   (decimals scaled to whole numbers first)
a:b = (a × k) : (b × k)                 for any k > 0
split a total T:  first = a ÷ (a + b) × T,  second = b ÷ (a + b) × T
new first term a′:  b′ = a′ × b ÷ a
a:b = c:d  ⇔  their simplest forms are the same  ⇔  a × d = b × c

Example

A 1920 × 1080 screen has the ratio 1920:1080. The greatest common divisor is 120, so it simplifies to 16:9; as a decimal that is 1.7778, and the width is 177.78% of the height.

Scaling 16:9 to a first term of 1280 gives a second term of 1280 × 9 ÷ 16 = 720, the familiar 1280 × 720.

Splitting 600 in the ratio 2:3 gives 2 ÷ 5 × 600 = 240 and 3 ÷ 5 × 600 = 360.

Comparing 16:9 with 4:3: 1.7778 is greater than 1.3333, so 16:9 is the wider shape.

Assumptions and limitations

• Both terms must be greater than zero, at most 1,000,000,000, and have at most six decimal places. Ratios with a zero or negative term are not handled.
• Decimal terms are made whole by multiplying both by the same power of ten before reducing, so 1.5:2 becomes 15:20 and then 3:4.
• Ratios are compared by their value a ÷ b; two ratios are equal exactly when their simplest forms match.
• Results are rounded to four decimal places for display; the simplest form is exact.

Frequently asked questions