Ratio Calculator

Ratios compare quantities. Whether you're scaling a recipe, comparing speeds, simplifying a ratio to its lowest terms, or solving a proportion for an unknown value, this calculator handles it all.

How to Use This Calculator

1. Simplify a ratio: Enter a:b → calculator reduces to lowest terms.
2. Solve a proportion: Enter three values in a:b = c:? (or a:b = ?:d) → calculator solves for the missing value.
3. Scale a ratio: Enter ratio and desired total → get each part's value.
4. Click Calculate for instant results.

Ratio Formulas

Simplify: Divide both terms by GCF. 24:36 → GCF = 12 → 2:3

Cross-multiplication (proportions): a/b = c/d → a × d = b × c → d = (b × c)/a

Example Calculations

Simplify 15:25: GCF(15,25) = 5 → 3:5

Solve proportion: 3:4 = 15:? → ? = (4 × 15)/3 = 20

Scale recipe: Ratio 2:3:5 totaling 600g → 2 parts = 120g, 3 parts = 180g, 5 parts = 300g

Real-World Applications

• Cooking: Scaling recipes up or down
• Maps: 1:50,000 scale means 1 cm = 500 m
• Finance: Price-to-earnings ratio, debt-to-equity ratio
• Architecture: Scale drawings and blueprints
• Mixing: Paint colors, concrete mixtures, chemical solutions

Common Mistakes to Avoid

• Confusing ratio with fraction — A ratio 3:4 is similar to 3/4 but refers to parts of a whole, not a division. In a 3:4 ratio, there are 3+4=7 total parts.
• Forgetting units must be the same — 500 cm : 2 m must be converted to the same unit (500 cm : 200 cm = 5:2) before simplifying.
• Cross-multiplying wrong terms — In a/b = c/d, ad = bc, not ac = bd.

Frequently Asked Questions

What is the difference between a ratio and a proportion?

A ratio is a comparison of two quantities (3:4). A proportion states that two ratios are equal (3:4 = 9:12). Solving a proportion means finding a missing value that makes two ratios equal.

How do I convert a ratio to a percentage?

Divide the first part by the sum of all parts, then multiply by 100. For 3:7 → 3/(3+7) = 0.30 = 30%.

What is the golden ratio?

The golden ratio φ ≈ 1.618 is a special ratio where a/b = (a+b)/a. It appears in art, architecture, nature (shell spirals, flower petal counts), and mathematics.

Conclusion

Ratios and proportions are foundational to math, science, cooking, and everyday problem-solving. This calculator handles simplification, proportion solving, and scaling — covering every ratio problem you're likely to encounter.

Related: Fraction Calculator | Percent Calculator | GCF Calculator