Ratio Calculator

Part-to-part is not part-to-whole

A ratio of 2:3 means five parts in total, two of one and three of the other — so the first is two fifths of the whole, not two thirds. This single confusion causes more ratio errors than anything else. When splitting 500 in the ratio 2:3, you divide by 5 to get one part, then multiply: 200 and 300.

Simplifying

Divide every term by the greatest common divisor of all of them. 18:24 becomes 3:4. With three or more terms the GCD must be common to all — 4:6:9 cannot be reduced despite the first two sharing a factor of 2. Ratios containing decimals or fractions are usually multiplied up to whole numbers first, since 1.5:2 reads better as 3:4.

Solving a proportion

Two equal ratios cross-multiply: if a/b = c/d then ad = bc. That single identity solves every missing-value proportion problem, from scaling a recipe to converting map distances. The only requirement is that the two ratios are set up in the same order on both sides — mixing the order is how proportion problems produce answers that are the reciprocal of the truth.

Ratios and rates behave differently

A ratio compares two quantities of the same kind and has no units: 3:2 boys to girls. A rate compares different kinds and keeps its units: 60 km per hour. Rates can be averaged with care; ratios often cannot. This distinction matters most when combining groups — two classes each with a 3:2 ratio combine to 3:2 only if the classes are the same size.

Aspect ratios are the common practical use

16:9, 4:3 and 3:2 describe shape independent of size, which is why they survive resizing. Preserving one when changing dimensions means scaling both terms by the same factor: 1920×1080 is 16:9, and so is 1280×720. Changing only one dimension distorts the image, which is what stretched video is.

Percentages, fractions and odds are the same information

A 1:4 ratio is one part in five, 20 percent, or 0.2. Odds are the exception worth watching: odds of 1:4 mean one success to four failures, so a 20 percent probability — while a 1 in 4 chance means 25 percent. Betting odds and probability ratios are read differently, and the gap catches people out consistently.