Simplify, complete, or scale ratios with step-by-step solutions.
Fill 3 of 4 values. Leave one blank to solve.
A ratio compares two or more quantities, showing how many times one value contains or is contained within the other. This calculator supports three common operations: completing a proportion (A:B = C:D), simplifying a ratio to its lowest terms using the greatest common divisor (GCD), and scaling a ratio by a constant factor.
Proportion: A/B = C/D → D = B×C/A. Simplification: A÷GCD / B÷GCD. Scale: A×k : B×k.
Simplifying a ratio means reducing both terms to their smallest possible integers while keeping the same proportion. For example, 12:18 simplifies to 2:3 because 12 and 18 share a GCD of 6.
In the proportion A:B = C:D, if three values are known, cross-multiply to find the fourth. For example, if A=2, B=4, C=6, then D = (B×C)/A = (4×6)/2 = 12, so 2:4 = 6:12.