Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Simplify a ratio to its lowest terms using GCD reduction.
2 : 3
This tool reduces a two-number ratio to its lowest terms by dividing both numbers by their greatest common divisor (GCD) -- the same math behind simplifying a fraction, applied to a ratio.
Enter the two numbers of your ratio (e.g. 12 and 18). The simplified ratio (e.g. 2:3) appears instantly.
The tool rounds each number to the nearest whole number, finds the greatest common divisor (GCD) using the Euclidean algorithm, and divides both numbers by it. The Euclidean algorithm repeatedly replaces the pair (a, b) by (b, a mod b) until the remainder is zero; the last non-zero value is the GCD. The tool starts with example values of 8 and 12 already in the fields, which simplify to 2 : 3. Both fields must contain non-zero numbers, otherwise you see a prompt to enter two non-zero numbers.
Simplified ratio = (A / GCD) : (B / GCD)
A simplified ratio expresses the same relationship in its smallest whole-number form. A recipe that uses 250 g of flour to 150 g of sugar has a ratio of 250 : 150, which reduces to 5 : 3. That makes it easy to scale: for 15 units of sugar you would use 25 of flour. Screens work the same way: 1920 : 1080 reduces to 16 : 9, a familiar aspect ratio. The simplified form does not change the proportions, only the size of the numbers used to express them.
The page says to clear decimals first, and this matters because the tool rounds inputs. Entering 2.5 and 4 would round 2.5 to 3 and report 3 : 4, which is not equivalent to 2.5 : 4. To keep the exact proportion, multiply both numbers by the same power of ten before entering them. For 2.5 : 4, multiply by 10 to get 25 : 40, which simplifies to 5 : 8. For 0.75 : 1.5, multiply by 100 to get 75 : 150, which simplifies to 1 : 2.
The tool handles two-part ratios only. For three or more parts, find the GCD of all the numbers, which you can do by simplifying two of them and then combining with the third by hand.
This tool works with whole numbers. For a ratio with decimals, multiply both sides by a power of 10 first to clear the decimal, then simplify.
The tool rounds each entry to a whole number before simplifying. Multiply both sides by 10, 100 or another power of ten first to remove decimals.
The two numbers share no common divisor other than 1, so the ratio is already in lowest terms.
Not directly. You can work out the GCD of all three numbers manually and divide each by it.
No. The ratio 2 : 3 compares two parts, while the fraction 2/3 describes one part of a whole. As parts of a total, 2 : 3 corresponds to 2/5 and 3/5.
Reference: NIST Weights and Measures