Ratio Calculator

Ratios describe how two quantities compare by division. This calculator solves proportions, where two ratios are set equal, and scales a ratio up or down while keeping its shape. Both tasks come up in cooking, mixing paint or concrete, map reading, resizing images and splitting costs.

What is Ratio?

A ratio compares two amounts by saying how many times one contains the other. It is usually written with a colon, as in 3 : 4, read three to four, but it can just as well be written as the fraction 3/4 or the decimal 0.75. A recipe that calls for 3 cups of flour to 4 cups of water has a flour-to-water ratio of 3 : 4. Order matters: the water-to-flour ratio is 4 : 3.

Like fractions, ratios can be simplified by dividing both terms by a common factor. A class of 12 girls and 16 boys has a girl-to-boy ratio of 12 : 16, which simplifies to 3 : 4 because both numbers divide by 4. Multiplying both terms by the same number gives an equivalent ratio, so 3 : 4, 6 : 8 and 600 : 800 all describe the same relationship. A ratio can also compare more than two quantities, such as the 1 : 2 : 3 proportions of cement, sand and gravel in a concrete mix.

A proportion is an equation stating that two ratios are equal: A : B = C : D. Writing the ratios as fractions, A/B = C/D, and cross-multiplying gives A × D = B × C, which lets you solve for any one missing term. If 3 : 4 = 600 : D, then 3D = 2,400 and D = 800. This is the familiar rule of three. It answers questions like how much paint a larger wall needs or how far 7 cm on a map is when 2 cm represents 5 km.

Scaling multiplies or divides both terms by the same factor. Enlarging 250 : 280 by 2.5 times gives 625 : 700, and shrinking it by 2.5 times gives 100 : 112. Scale models, blueprints and image resizing all rely on this. Keep in mind that while lengths scale by the factor, areas scale by its square and volumes by its cube.

Typical Aspect Ratios and Sizes of Screens and Videos

An aspect ratio is the ratio of an image's width to its height. Keeping it fixed when resizing prevents pictures from looking stretched or squashed. Most modern televisions, monitors and online video use 16 : 9, which replaced the older 4 : 3 standard of analog TV. Cinema often uses wider formats, and phones held upright show tall ratios such as 9 : 16 or 9 : 19.5.

To find a missing dimension at a given aspect ratio, solve a proportion. A 16 : 9 video that is 1,280 pixels wide must be 1,280 × 9 ÷ 16 = 720 pixels tall. Common pairings are listed below.

Frequently asked questions