Free Ratio Calculator Online
Simplify ratios, solve proportions, and scale values with this free ratio calculator. Get instant results with step-by-step breakdowns showing the greatest common divisor and full calculation path.
Simplified Ratio
Original 120 : 80
Step-by-Step
- 1. Find GCD of 120 and 80 = 40
- 2. Divide both by 40: 120 / 40 = 3
- 3. 80 / 40 = 2
- 4. Simplified ratio = 3 : 2
How the Ratio Calculator Works
A ratio compares two or more quantities. The ratio calculator uses the Euclidean algorithm to find the greatest common divisor (GCD), then divides both terms to produce the simplified ratio. For proportions, it applies cross-multiplication to find the missing value. Scaling multiplies each term by your chosen factor while preserving the relationship between quantities. Every ratio calculator result includes the decimal equivalent and percentage.
When to Use a Ratio Calculator
Use this ratio calculator for cooking recipe conversions, mixing solutions, map scale calculations, aspect ratio adjustments for images, financial comparisons, and academic math problems. Architects use ratios for scale drawings. Investors compare P/E ratios. Teachers assign ratio problems. Wherever two quantities relate, the ratio calculator helps you find the simplest expression and solve for unknowns.
Ratio Formulas & Reference
| Formula | Example | Use Case |
|---|---|---|
| A : B simplified | 120 : 80 = 3 : 2 (GCD = 40) | Simplify any ratio to lowest terms |
| A/B = C/D | 3/4 = 12/? => ? = 16 | Solve for missing proportion value |
| A*N : B*N | 2:5 * 3 = 6:15 | Scale a ratio by a factor |
| GCD(A, B) | GCD(120, 80) = 40 | Find greatest common divisor |
Frequently Asked Questions
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