Free Ratio Calculator
Simplify ratios to lowest terms, solve proportion equations (A:B = C:D), and distribute amounts in any ratio. Includes percentage conversion and GCD-based simplification. Free, private — all calculations run in your browser.
About This Ratio Calculator
The Ratio Calculator covers the three core ratio operations you encounter in everyday life and professional work: simplifying a ratio to its lowest terms, solving a proportion equation when one value is missing, and distributing a total amount according to a ratio. Whether you are scaling a recipe, designing to spec, analysing financial data, or mixing materials, this tool handles the arithmetic instantly and accurately.
The Formulas — How They Work
Simplifying a ratio — divide both terms by their Greatest Common Divisor:
Solving a proportion — equivalent ratios satisfy A/B = C/D. Cross-multiplication gives AD = BC, so any missing value can be found:
Converting to percentage — each part's share of the total:
Ratios vs Fractions vs Percentages
These three are deeply related but represent different ideas. A ratio A:B compares two quantities to each other — the total is A+B parts. A fraction A/B represents A as a proportion of B — B is the whole. A percentage is always out of 100. Converting between them: ratio 3:2 → fraction 3/5 of the whole (not 3/2) → 60% of the total. Understanding this distinction prevents errors when working with recipes, financial splits, and mixture concentrations.
Real-World Applications
- •Cooking and baking: scale ingredient quantities while preserving the exact taste profile
- •Map reading: convert map distances to real distances using the stated scale
- •Financial analysis: debt-to-equity ratio, current ratio, price-to-earnings ratio
- •Construction and carpentry: ensure structural members maintain load-bearing proportions
- •Photography: maintain aspect ratios when printing or displaying images at different sizes
- •Chemistry: prepare solutions at correct molar concentrations by maintaining reagent ratios
Privacy Notice
All calculations in this calculator are performed entirely in your browser. No data you enter is transmitted to any server, stored in any database, or shared with third parties. See our Privacy Policy for full details.
When to Use This Calculator
Scale any recipe up or down while preserving ingredient ratios. If a recipe for 4 needs 2 cups of flour, find exactly how much to use for 10 servings using proportion solving.
Convert between map distances and real-world distances using the map's stated scale ratio (e.g., 1:50,000 means 1 cm = 500 m). Solve for either value.
Maintain aspect ratios when resizing images, designing banners, or cropping video. Ensure 16:9 or 4:3 proportions are preserved across different pixel dimensions.
Calculate the correct volumes when mixing chemicals, paints, fuels, or cleaning solutions to achieve a target concentration ratio.
Divide revenue, profits, or costs among partners, shareholders, or departments according to agreed ratio splits — with automatic calculation of each party's exact share.
💡 Pro Tips
Always simplify ratios to their lowest terms first — it makes the numbers easier to work with and reveals the fundamental relationship. To find the GCD, use the Euclidean algorithm: GCD(48, 36) = GCD(36, 12) = GCD(12, 0) = 12, so 48:36 simplifies to 4:3.
The golden ratio 1:1.618 (φ) appears naturally in art, architecture, and nature. Designers use it to create proportions that are universally considered aesthetically pleasing. A rectangle with sides in ratio 1:φ is a "golden rectangle." Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21...) produce increasingly accurate approximations of φ as adjacent-number ratios.
Know your screen aspect ratios for design work: 16:9 for all HD/4K video and YouTube thumbnails, 4:3 for traditional presentations and iPad, 1:1 for square social media, 9:16 for vertical mobile stories. Always verify output dimensions maintain the ratio using the proportion solver — a 2560×1440 canvas is exactly 16:9 (÷ 160 = 16:9).
Cross-multiplication is the fastest way to solve any proportion. If you know three of the four values in A:B = C:D, multiply across the diagonal of the known pair and divide by the remaining known value. This works because AD = BC always holds for equivalent ratios, and rearranging gives any missing variable directly.
Frequently Asked Questions
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