What is the Ratio of 3 Numbers Calculator?
This tool reduces a three-part ratio, written as A:B:C, to its simplest equivalent form. Just like simplifying a fraction, a ratio is in lowest terms when no whole number greater than 1 divides all three parts. For example, 12:18:30 simplifies to 2:3:5, which describes the same proportional relationship using the smallest possible whole numbers.
How to use it
Enter the three quantities in the A, B and C fields and submit. The calculator computes the greatest common divisor (GCD) of all three values and divides each term by it. Decimal inputs such as 1.5:3:4.5 are supported — the values are first scaled up to whole numbers, then reduced.
The formula explained
The greatest common divisor of three numbers is found by chaining the two-number GCD: \(g = \gcd(\gcd(a, b), c)\). The simplified ratio is then $$\frac{a}{g} : \frac{b}{g} : \frac{c}{g}.$$ Because \(g\) divides every term exactly, the new ratio represents exactly the same proportion.
Worked example
Take 12:18:30. The GCD of 12 and 18 is 6; the GCD of 6 and 30 is 6, so \(g = 6\). Dividing each term: \(12/6 = 2\), \(18/6 = 3\), \(30/6 = 5\). The simplest form is 2:3:5.
FAQ
Can I enter decimals? Yes. Values like 1.5:3:4.5 are scaled to whole numbers (15:30:45) and reduced to 1:2:3.
What if the ratio is already simplest? If the GCD is 1, the ratio is returned unchanged — for example 4:9:25 stays 4:9:25.
Does order matter? The order of the parts is preserved; only the scale changes, so A:B:C maps directly to the reduced A:B:C.
