A ratio compares two parts. 12 : 18 means twelve of the first for eighteen of the second. Those parts reduce to 2 : 3 by dividing by 6. A proportion says two ratios are equal: 2 : 5 = 8 : X, so X is 20. A ratio calculator that tries to become a general algebra solver hides those two jobs. This page keeps them as two modes: simplify A : B, and find X in A : B = C : X.
Simplification uses integer reduction after decimals are scaled. 1.5 : 2.5 becomes 3 : 5. The missing-term mode uses X = (B × C) ÷ A and shows an integer when the division is exact, or a reduced fraction when it is not. A cannot be 0 in that mode, because the proportion would divide by zero. 0 : 0 is not a ratio.
Ratios are kin to fractions and to GCD. Reducing 12 : 18 is the same gcd step you would use on 12/18. Cross-links: the Fraction Calculator for arithmetic on fractions, and the GCD & LCM Calculator when you only need the divisor or multiple.
Labels stay A, B, and C so the proportion is readable. The result is a single line: either a reduced ratio or X = …
Simplify: scale A and B to integers, then divide by gcd(|A|, |B|). Proportion: A/B = C/X, so X = B×C / A, then reduce the fraction B×C over A. That is the relationship between a ratio and a proportion: a proportion is two equal ratios. This is not a system-of-equations solver and not a three-part recipe mixer.
Simplify 12 : 18 → 2 : 3. Simplify 0 : 4 → 0 : 1. Find X for 2 : 5 = 8 : X → X = 20. Find X for 2 : 5 = 3 : X → X = 15/2. A = 0 in missing mode is rejected. 0 : 0 is rejected.
12 : 18 ÷ 6 = 2 : 3
2 / 5 = 8 / X → X = 20Recipe scaling is the missing-term mode in disguise. If a mix is 2 parts oil to 5 parts vinegar and you have 8 units of oil, that is 2 : 5 = 8 : X for vinegar. If you instead know the total volume, you are splitting a whole into parts, which is a different setup: you need the sum of the parts first. This page does not take a total and a ratio in one step, because that would hide whether X is a part or a whole.
To add or divide the fractions that sit behind a ratio, open the Fraction Calculator. To see only gcd(12, 18) or lcm(12, 18), use the GCD & LCM Calculator.
Divide both parts by their greatest common divisor after scaling decimals to integers.
A proportion. X = (B × C) ÷ A. A cannot be 0.
Yes. It simplifies to 0 : 1. 0 : 0 is rejected.
A ratio A : B is related to the fraction A/B, but the page talks in parts. Use the Fraction Calculator for add, subtract, multiply, and divide.
