Two tools in one: simplify a ratio like 18:24 down to lowest terms, or solve a proportion A:B = C:X for the missing fourth value. Decimals are handled automatically.
How the ratio calculator works
A ratio compares two quantities: 18:24 says "for every 18 of the first thing, there are 24 of the second." Simplifying keeps that relationship but shrinks the numbers — divide both sides by their greatest common divisor and 18:24 becomes 3:4. If the ratio has decimals, the calculator first scales both sides up by 10, 100, and so on until they're whole numbers, then simplifies. Proportion mode uses cross-multiplication to find the missing fourth value in A:B = C:X.
The formulas
Simplified ratio = (A ÷ GCD) : (B ÷ GCD)
A : B = C : X ⇒ X = (B × C) ÷ A
GCD is the greatest common divisor of A and B. The proportion rule comes from cross-multiplying the equal fractions A/B = C/X, which gives A·X = B·C.
Worked examples
Simplify 18:24 — the GCD of 18 and 24 is 6, so 18:24 = 3:4.
Simplify 2.5:1.5 — multiply both by 10 to get 25:15, whose GCD is 5, so the answer is 5:3.
Solve 3:4 = 9:X — cross-multiply: X = (4 × 9) ÷ 3 = 12. Check: 3/4 = 9/12. ✓
The scaling trap
The most common ratio mistake is changing only one side. If a mortar mix calls for cement and sand at 1:3 and you double the cement, you must double the sand too — a ratio only survives multiplication or division applied to both sides. Adding the same amount to both sides, on the other hand, wrecks it: 1:3 plus one on each side is 2:4 = 1:2, a completely different mix. When scaling anything by ratio, multiply — never add.
Frequently asked questions
How do I simplify a ratio?
Divide both sides by their greatest common divisor (GCD). For 18:24 the GCD is 6, so it simplifies to 3:4. If the ratio contains decimals, first multiply both sides by 10, 100, etc. until both are whole numbers, then divide by the GCD — 2.5:1.5 becomes 25:15, which simplifies to 5:3.
How do I solve a proportion like 3:4 = 9:X?
Cross-multiply: in A:B = C:X, the product of the outer terms equals the product of the inner ones, so X = (B × C) ÷ A. For 3:4 = 9:X that's X = (4 × 9) ÷ 3 = 12. It works because equal ratios are equal fractions: 3/4 = 9/12.
What's the difference between a ratio and a fraction?
A ratio compares two quantities side by side (3 parts flour to 4 parts water), while a fraction expresses one quantity as a part of a whole. They're closely related: the ratio 3:4 corresponds to the fraction 3/4 when comparing the first quantity to the second, but 3/7 when comparing it to the total.
Can a ratio have decimals in it?
Yes — 2.5:1.5 is a perfectly valid ratio. But convention prefers whole numbers, so you scale both sides up until the decimals disappear, then simplify: 2.5:1.5 = 25:15 = 5:3. This calculator does that scaling for you automatically.
How do I scale a recipe or mixture using ratios?
Set up a proportion with the known ratio on one side and your new quantity on the other. If a recipe uses flour and water at 3:4 and you have 9 cups of flour, solve 3:4 = 9:X to find you need 12 cups of water. That's exactly what this calculator's proportion mode does.