Ratio Calculator
Simplify ratios and solve equivalent ratio proportions A : B = C : D.
Ratio Simplifier (A : B)
Parts, wholes, and cross-multiplication
A ratio compares quantities: 3:2 means three of one for every two of another. The trap is thata ratio is not a fraction of the whole. In a 3:2 mix the first part is 3/5 of the total, not 3/2 — the denominator of the fraction is the sum of the parts, not the other part. Mixing these up is the most common ratio error there is.
Ratios simplify like fractions, by dividing through by the GCF, so 18:12 reduces to 3:2 and both describe the same relationship. Scaling multiplies every term by the same factor, which is how a recipe for four becomes one for six. To split a total in a given ratio, add the parts to get the number of shares, divide the total by that, then multiply out: £200 split 3:2 is five shares of £40, giving £120 and £80.
A proportion sets two ratios equal, and is solved by cross-multiplication — from3/4 = x/20 you get 4x = 60, so x = 15. That single move underpins unit conversion, scale drawings, map distances and most everyday "if this then how much of that" problems.
Frequently Asked Questions
How do you solve a ratio proportion A/B = C/D?
Cross-multiply: A × D = B × C. If one value is unknown (X), solve algebraically (e.g. X = B × C / A).
How do I simplify a ratio?
Divide every term by the greatest common factor. 18:24 has a GCF of 6, simplifying to 3:4. Ratios with decimals should first be scaled to whole numbers by multiplying through by a power of ten.
How do I solve a proportion?
Cross-multiply: if a/b = c/d then ad = bc, so any missing term can be isolated. Scaling a 3:4 recipe up to 12 parts of the first ingredient means the second becomes 16, since 3/4 = 12/x gives x = 16.
What is the difference between a ratio and a fraction?
A ratio compares two quantities, which may be parts of a whole or entirely separate things. A fraction always expresses a part of a single whole. A 3:4 ratio of boys to girls means 3/7 of the class are boys - the fraction and the ratio carry different denominators.