Ratio calculator
Three ratio sums in one place. Each answer updates as you type.
Runs in your browser. Nothing is sent or saved.
Simplifying a ratio
A ratio is in its simplest form when its parts have no common factor left. Divide every part by their greatest common divisor: 1920 and 1080 are both divisible by 120, so 1920:1080 is 16:9, the shape of most screens. Ratios with decimals are first multiplied to whole numbers: 1.5:2 becomes 15:20 and then 3:4. Ratios with three or more parts work the same way, for example 12:18:30 is 2:3:5.
| Ratio | Simplest form | As 1 : n |
|---|---|---|
| 1920:1080 | 16:9 | 1 : 0.5625 |
| 1080:1350 | 4:5 | 1 : 1.25 |
| 2560:1080 | 64:27 | 1 : 0.421875 |
| 1.5:2 | 3:4 | 1 : 1.333333 |
| 12:18:30 | 2:3:5 | 1 : 1.5 : 2.5 |
Screens sold as "21:9" are usually 2560 × 1080, which is exactly 64:27, about 2.37 to 1; 21:9 is a rounded marketing name.
Finding the missing number
In a proportion a:b = c:d, the cross products are equal: a × d = b × c. So the missing number is the product of the two diagonal numbers divided by the one across from it. To keep a 16:9 picture 1280 pixels wide, the height is 9 × 1280 ÷ 16 = 720. A recipe for 4 people that uses 300 g of flour needs 300 × 6 ÷ 4 = 450 g for 6 people.
Splitting an amount
Add the parts of the ratio, divide the amount by that total, then multiply by each part. Splitting $100 in the ratio 3:2: there are 5 parts, each worth $20, so the shares are $60 and $40, or 60% and 40%. With 1:1:1 the shares are a third each, 33.33 when rounded to cents, so in money one share has to take the extra cent.
Questions
How do I write a ratio here?
Use a colon (16:9), the word "to" (1 to 4) or a slash (3/2). Three or more parts work in the Simplify and Split boxes: 2:3:5.
What is the difference between a ratio and a fraction?
A ratio compares parts with each other, a fraction compares a part with the whole. In a class with 12 girls and 18 boys, the ratio of girls to boys is 12:18, or 2:3, while girls are 12/30, or 2/5, of the class. The fraction converter turns 2/5 into 0.4.
Can a ratio have decimals or be zero?
Decimals are fine and are simplified to whole numbers. A part of zero isn't a useful ratio, so the calculator asks for numbers above zero.