Ratio Calculator
Simplify ratios, solve proportions and split a total by ratio, without the part-to-whole confusion.
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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.
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Frequently Asked Questions
Does a 2:3 ratio mean two thirds?
No. It means five parts in total, so the first quantity is two fifths of the whole. Confusing part-to-part with part-to-whole is the most common ratio error.
How do I split an amount by a ratio?
Add the parts to get the total number of shares, divide the amount by that, then multiply by each part. Splitting 500 in 2:3 gives 200 and 300.
How do I solve a proportion?
Cross-multiply: if a/b = c/d then ad = bc. Both ratios must be written in the same order, or the answer comes out as the reciprocal of the truth.
What is the difference between a ratio and a rate?
A ratio compares quantities of the same kind and has no units; a rate compares different kinds and keeps them. Rates can often be averaged, ratios usually cannot.
Are odds the same as probability?
No. Odds of 1:4 mean one success to four failures, which is 20 percent, whereas a 1 in 4 chance is 25 percent. The two are read differently.
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How to Use
Enter A:B to simplify, or fill three of A:B = C:D to solve for the missing one (leave it blank).
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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