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A ratio compares two or more quantities by division. The ratio 8:12 means "8 to 12," and simplifies to 2:3 by dividing both parts by their greatest common divisor (GCD). Ratios are used in recipes, maps, finance, engineering, and probability.
This calculator simplifies any ratio to its lowest terms, scales a ratio to a target value, and displays equivalent ratios. The simplification algorithm finds the GCD of all parts and divides through — the same method used to reduce fractions.
For example, the ratio 15:20:25 simplifies by GCD(15,20,25) = 5 to give 3:4:5. Scaling the ratio 2:3 so the first part equals 10 gives 10:15.
Simplified Ratio = a/GCD(a,b) : b/GCD(a,b) | GCD by Euclidean: GCD(a,b) = GCD(b, a mod b)
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This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.