Ratio Calculator
Simplify a ratio such as 8:12 to its lowest terms, or solve a proportion a:b = c:x for the missing number. Handles decimals and three-part ratios, and shows the decimal value.
Calculator
How it's calculated
The greatest common divisor of 8 : 12 is 4.
Dividing every term by the GCD gives 2 : 3.
About this calculator
A ratio compares two (or three) quantities of the same kind — 8 cups of flour to 12 cups of water is the ratio 8 : 12. This calculator does the two jobs people reach for most. In simplify mode it reduces a ratio to its lowest whole-number terms (8 : 12 becomes 2 : 3) and reports the decimal value A ÷ B. In proportion mode it solves a true proportion A : B = C : x for the one term you are missing, which is exactly how you scale a recipe up, convert a map distance, or split a sum in a given ratio. Decimals such as 2.5 : 5 are handled by scaling every term up to whole numbers before reducing.
How to read your results
In simplify mode the large figure is the ratio in its simplest form, with the greatest common divisor (GCD) and the decimal value A ÷ B shown beneath it; a ratio is already in lowest terms when its GCD is 1. Add a third value to reduce a three-part ratio such as 2 : 4 : 6 to 1 : 2 : 3. In proportion mode the headline is the missing term x, and the proportion row restates the full statement A : B = C : x with the gap filled in, so you can sanity-check that both halves really are equal.
How it's calculated
To simplify, each term is first scaled to a whole number by a common power of ten (so 2.5 : 5 becomes 25 : 50), the greatest common divisor of the scaled terms is found with the Euclidean algorithm, and every term is divided by that GCD. The decimal value is simply A ÷ B. To solve a proportion A : B = C : x, the calculator cross-multiplies — A × x = B × C — and rearranges to x = (B × C) ÷ A. The same rearrangement finds any single missing term once the other three are known.
Worked example
Simplify 8 : 12, then solve the proportion 2 : 3 = 10 : x.
The greatest common divisor of 8 and 12 is 4, so 8 : 12 reduces to 2 : 3, with a decimal value of 8 ÷ 12 ≈ 0.6667. For the proportion, cross-multiplying gives x = (3 × 10) ÷ 2 = 15, so 2 : 3 = 10 : 15.
Frequently asked questions
How do I simplify a ratio to its lowest terms?
Find the greatest common divisor (GCD) of the terms and divide each term by it. For 8 : 12 the GCD is 4, so 8 ÷ 4 : 12 ÷ 4 gives 2 : 3. A ratio is already in lowest terms when the only number that divides every term is 1.
Can I simplify a ratio that contains decimals?
Yes. The calculator scales every term up by a common power of ten until they are whole numbers, then reduces. So 2.5 : 5 becomes 25 : 50, which reduces to 1 : 2. The result is always expressed in whole numbers.
How do I solve a proportion for the missing number?
Write it as A : B = C : x and cross-multiply, so A × x = B × C, which rearranges to x = (B × C) ÷ A. For 2 : 3 = 10 : x that is x = (3 × 10) ÷ 2 = 15. Switch to "Solve a proportion" mode and enter A, B and C.
What is the decimal value of a ratio?
It is the first term divided by the second, A ÷ B. For 7 : 2 the decimal value is 3.5, meaning the first quantity is 3.5 times the second. It is shown only for two-part ratios, since a three-part ratio has no single decimal value.
Sources
Reviewed by the YouCalc Team · Last reviewed
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