Three-Number Ratio Simplifier
Simplify a ratio of three numbers, a : b : c, to its lowest whole-number terms and see each part as a share of the whole.
How it works
g = gcd(a, b, c) · simplified = a/g : b/g : c/g · share = part ÷ (a + b + c) × 100
A ratio of three quantities is reduced the same way a fraction is: divide every term by the greatest common divisor of all three. The greatest common divisor of the trio is found by taking the GCD of the first two, then the GCD of that result with the third. Converting each part to a percentage of the total shows how the whole is split, which is handy for recipes, mixes and budgets.
Worked example
For 12 : 18 : 30, gcd(12, 18) = 6 and gcd(6, 30) = 6, so divide each by 6 to get 2 : 3 : 5. As shares of the total 60, the parts are 20%, 30% and 50%.
Frequently asked questions
How do you simplify a ratio with three numbers?
Find the greatest common divisor of all three numbers, then divide each number by it. For 12 : 18 : 30 the GCD is 6, giving 2 : 3 : 5 — the smallest whole numbers in the same proportion.
What if one of the parts is zero?
A zero part stays zero (for example 4 : 0 : 6 simplifies to 2 : 0 : 3). The calculator only needs at least one non-zero part to work; an all-zero ratio has no meaning.
Why show each part as a percentage?
The simplified ratio tells you the proportions, and the percentages tell you each part’s slice of the whole. Together they make it easy to scale the mix up or down to any total amount.
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This calculator is for educational purposes. Double-check important results before acting on them.