Ratio Calculator

What is a ratio?

A ratio compares two quantities, showing how much of one there is for every amount of another. It is written with a colon (3:4), as a fraction (3/4), or in words ("3 to 4"). A part-to-part ratio compares two separate parts, for example 3 boys to 4 girls, while a part-to-whole ratio compares one part to the total, such as 3 boys out of 7 children. Ratios appear everywhere: recipes, maps and scale models, screen sizes, mixing fuel, and odds. Because a ratio is only a comparison, the same relationship can be written many equivalent ways, so 1:2, 2:4 and 50:100 are all the same ratio.

How to simplify and solve ratios

To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For 18:24 the GCD is 6, so 18:24 = 3:4. Two ratios are equal when they form a proportion (a:b = c:d), and you find a missing value by cross-multiplying, since a times d equals b times c. To turn a ratio into a fraction, write the first number over the second (3:4 becomes 3/4); into a decimal, divide them (3 divided by 4 = 0.75); and into a part-to-whole percentage, divide each part by the total (3:2 gives 3 of 5 = 60% and 2 of 5 = 40%). This calculator simplifies any ratio and solves a proportion for a missing term.

Example

A photo is 1920 pixels wide and 1080 tall. The GCD of 1920 and 1080 is 120, so the aspect ratio simplifies to 16:9, the standard widescreen shape. To scale a 3:4 recipe so the first part becomes 9, set 3:4 = 9:x and cross-multiply: 3 times x = 4 times 9, so x = 12, giving 9:12 (which is still 3:4).