Ratio Calculator
Ratio Calculator
Simplify: Reduce a ratio to its lowest terms.
Select a calculation type, enter your values, and click "Calculate" to see the results
Understanding Ratios and Proportions
What is a Ratio?
A ratio compares two quantities by division, showing their relative sizes. Written as a:b (read as "a to b"), ratios express relationships like ingredient proportions, screen dimensions, or mixing instructions. For example, a 3:2 ratio means for every 3 units of the first quantity, there are 2 units of the second.
Key Ratio Concepts
- Simplification: Reducing a ratio to its lowest terms (12:8 โ 3:2)
- Equivalent Ratios: Different ratios representing the same relationship (1:2 = 2:4 = 3:6)
- Part-to-Part: Comparing two separate parts (boys:girls = 3:2)
- Part-to-Whole: Comparing one part to the total (boys:total = 3:5)
- Proportions: Two equal ratios forming an equation (a:b = c:d)
How to Use This Ratio Calculator
Simplify Ratios
Reduce any ratio to its simplest form by finding the greatest common divisor (GCD).
Scale Ratios
Multiply or divide both parts of a ratio by the same factor to scale up or down.
Solve Proportions
Find the missing value in a proportion using cross-multiplication.
Golden Ratio
Calculate dimensions using the golden ratio (1.618:1) for harmonious proportions.
Real-World Applications
๐ณ Cooking & Baking
Scale recipes while maintaining proper ingredient ratios. A bread recipe with a 5:3 flour-to-water ratio will have the same texture whether you use 500g:300g or 1000g:600g. Perfect for adjusting serving sizes or converting between metric and imperial units.
๐จ Art & Design
The golden ratio (ฯ โ 1.618) creates visually appealing compositions. Used by artists from Da Vinci to modern graphic designers, it's found in logo design, page layouts, and photography. Apply it to determine canvas sizes, crop photos, or design UI elements.
๐ฅ๏ธ Screen & Image Ratios
Common aspect ratios include 16:9 (HD/4K), 4:3 (classic TV), 21:9 (ultrawide), and 1:1 (Instagram). Understanding these helps resize images without distortion, choose the right monitor, or export videos for different platforms. A 1920ร1080 image is 16:9.
๐๏ธ Architecture & Engineering
Blueprint scales use ratios like 1:100 (1cm on paper = 100cm in reality). Mixing concrete requires precise ratios (e.g., 1:2:3 for cement:sand:aggregate). Engineers use gear ratios to calculate mechanical advantage and speed reductions.
๐ฐ Finance & Business
Financial ratios analyze business health: debt-to-equity ratios assess leverage, price-to-earnings ratios value stocks, and profit margins compare revenue to costs. Investment portfolios use asset allocation ratios (e.g., 60:40 stocks-to-bonds).
๐งช Science & Medicine
Dilution ratios prepare chemical solutions (1:10 means 1 part solute to 10 parts solvent). Medical dosages use body-weight ratios. Laboratory experiments require precise ingredient ratios for reproducible results.
Common Ratios Reference Guide
Screen Aspect Ratios
- 16:9 โ HD, Full HD, 4K, 8K
- 16:10 โ Professional monitors
- 21:9 โ Ultrawide monitors
- 4:3 โ Classic TV, old monitors
- 1:1 โ Square (Instagram posts)
- 9:16 โ Vertical video (TikTok)
Photography Ratios
- 3:2 โ DSLR standard (e.g., 6000ร4000)
- 4:3 โ Micro Four Thirds
- 1:1 โ Square format
- 5:4 โ Large format
- 8:10 โ Portrait prints
Paper Sizes (ISO 216)
- โ2:1 โ A-series (A4, A3, etc.)
- 1:1.414 โ Same ratio when folded
- 8.5:11 โ US Letter
- 11:17 โ Tabloid
Golden Ratio Applications
- 1.618:1 โ Classic golden ratio
- Parthenon facade proportions
- Mona Lisa composition
- Apple logo design
- Credit card dimensions
- Book page layouts
Cooking Ratios
- 2:1 โ Rice to water
- 3:2:1 โ Vinaigrette (oil:vinegar:other)
- 5:3 โ Bread (flour:water)
- 1:1:1 โ Pound cake
- 3:2:1 โ Concrete mix
Map & Model Scales
- 1:24,000 โ USGS topo maps
- 1:50,000 โ Hiking maps
- 1:100 โ Architectural plans
- 1:12 โ Dollhouse scale
- 1:64 โ Matchbox cars
Frequently Asked Questions
What is a ratio and how do you simplify it?
A ratio is a comparison between two numbers, written as a:b. To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, 12:8 simplifies to 3:2 because both numbers can be divided by 4. Simplified ratios make comparisons easier and are essential in cooking, design, and mathematics.
How do you solve proportions?
To solve a proportion a:b = c:x, use cross-multiplication: x = (b ร c) / a. For example, if 3:4 = 6:x, then x = (4 ร 6) / 3 = 8. This method is useful for scaling recipes, converting units, and solving mathematical word problems.
What is the golden ratio and why is it important?
The golden ratio (ฯ) is approximately 1.618:1, a mathematical constant found throughout nature, art, and architecture. It creates aesthetically pleasing proportions and appears in the Fibonacci sequence, seashells, flower petals, and classic architecture like the Parthenon. Designers use it to create harmonious compositions.
How do I convert a ratio to a percentage?
To convert a ratio to percentages: 1) Add both parts of the ratio, 2) Divide each part by the total, 3) Multiply by 100. For example, 3:2 โ Total = 5 โ First part: (3/5) ร 100 = 60%, Second part: (2/5) ร 100 = 40%. This is useful for understanding proportional distributions.
How do aspect ratios work for screens and images?
Aspect ratio is the width-to-height ratio of screens or images. Common ratios include 16:9 (widescreen HD), 4:3 (standard TV), 21:9 (ultrawide), and 1:1 (square for Instagram). For example, a 1920ร1080 screen has a 16:9 aspect ratio (1920รท1080 = 16รท9). Maintaining aspect ratios prevents image distortion.
Can I use ratios for recipe scaling?
Yes! Ratios are perfect for scaling recipes. If a recipe serves 4 people and uses 2 cups flour to 1 cup sugar (2:1 ratio), to serve 8 people, multiply both by 2: 4 cups flour to 2 cups sugar. Our calculator helps maintain proper ingredient proportions when adjusting serving sizes.
External Resources & Further Reading
Educational Resources
- Khan Academy - Ratios and Proportions
Free video lessons and practice problems on ratios
- Math Is Fun - Understanding Ratios
Clear explanations with visual examples
Design & Golden Ratio
- Canva - Golden Ratio in Design
Practical guide for designers
- Wikipedia - Golden Ratio
Comprehensive mathematical and historical reference
Note: These external links are provided for educational purposes. We are not affiliated with these organizations.