Ratio Calculator — Simplify Ratios, Solve Proportions & Convert
Use our ratio simplifier to reduce any ratio to its simplest form, solve proportions, scale ratios up or down, and convert ratios to fractions, decimals, and percentages. Includes real-world examples for cooking, finance, design, and more.
What is a Ratio?
A ratio is a comparison of two or more quantities. Written as a:b (read "a to b"), it tells you how much of one thing there is compared to another. A 2:1 flour-to-sugar ratio means for every 2 cups of flour, you need 1 cup of sugar.
Important: A ratio describes the relationship between parts, not a part-to-whole relationship like a fraction. In a 2:1 ratio, the total is 3 parts (2+1), not 2 out of 1.
How to Simplify Ratios
Reducing a ratio to its simplest form means rewriting it so both parts are the smallest whole numbers that keep the same proportion. Every ratio has exactly one simplest form: 8:12, 16:24, and 2:3 all express the same relationship, but only 2:3 is in simplest form.
Step-by-Step Method
- Find the GCD (Greatest Common Divisor) of the numbers in the ratio.
- Divide every part of the ratio by the GCD.
- The result is the ratio in its simplest form.
Worked Examples
- 8:12 → GCD = 4 → 8÷4 : 12÷4 → 2:3
- 24:36 → GCD = 12 → 24÷12 : 36÷12 → 2:3
- 4:12 → GCD = 4 → 4÷4 : 12÷4 → 1:3
- 18:45 → GCD = 9 → 18÷9 : 45÷9 → 2:5
- 6:9:15 → GCD = 3 → 6÷3 : 9÷3 : 15÷3 → 2:3:5
How to Solve Proportions
A proportion states that two ratios are equal: a:b = c:d. To find a missing value, use cross-multiplication.
Cross-Multiplication Formula
Example: If 2:3 = 8:x, then 2x = 24, so x = 12.
Ratio Formulas Explained
Simplifying Ratios
A:B → (A÷GCD) : (B÷GCD)
Example: 8:12 → GCD=4 → 2:3
Proportions (Missing Value)
A:B = C:D → D = (B × C) ÷ A
Example: 2:3 = 8:? → ? = 12
Scaling Ratios
A:B → (A×F) : (B×F)
Example: 2:3 × 4 = 8:12
Ratio Conversions
Fraction: A/B | Decimal: A÷B | %: (A÷B)×100
Example: 3:4 = 3/4 = 0.75 = 75%
Real-World Ratio Applications
Recipe Scaling
A pancake recipe calls for a 2:1 ratio of flour to milk. You want to use 3 cups of flour. How much milk? 2:1 = 3:x → x = 1.5 cups of milk.
Aspect Ratios
A 55-inch TV has a 16:9 aspect ratio. The height is 55 × (9/16) = 30.9 inches. The diagonal measurement (55 inches) is the hypotenuse of a right triangle where the sides are in a 9:16 ratio.
Financial Ratios
Debt-to-Income: A bank requires a DTI ratio of 36:100 (36%). If your monthly debt is $1,800 and gross income is $5,000: DTI = 1,800:5,000 = 36:100 = 36% — you qualify.
P/E Ratio: A stock trading at $150 per share with earnings of $5 per share has a P/E ratio of 30:1. The market pays $30 for every $1 of earnings.
Map Scales
A map scale of 1:50,000 means 1 inch on the map = 50,000 inches on the ground (about 0.79 miles). Two cities 4 inches apart on the map are 3.16 miles apart.
Mixing Ratios
A cleaning concentrate requires a 10:1 water-to-concentrate ratio. To make 1 liter: water = 909ml, concentrate = 91ml.
Common Ratio Mistakes
Treating Ratios as Fractions
A 1:2 ratio doesn't mean "one out of two" — it means one part to two parts (total 3).
Not Simplifying
24:16 and 6:4 and 3:2 are the same ratio — always simplify for comparison.
Confusing Part:Part with Part:Whole
2:3 is a part:part ratio. 2/5 is the fraction of the whole.
Key Takeaways
- Ratio = a:b — a comparison of two quantities
- Simplify by dividing by the GCD of all parts
- Cross-multiply to solve proportions
- Ratios describe relationships between parts, not parts of a whole
- Use the calculator above for instant simplification and proportion solving
Ratio vs. Fraction vs. Proportion
| Concept | Format | Example | What It Tells You |
|---|---|---|---|
| Ratio | a:b | 3:2 | For every 3 of A, there are 2 of B (total 5 parts) |
| Fraction | a/b | 3/5 | 3 parts out of a total of 5 |
| Proportion | a:b = c:d | 1:2 = 3:6 | Two ratios are equal |
Common Aspect Ratios Reference
Aspect ratios are used in photography, video, screen design, and printing.
| Ratio | Name | Use Case | Example Resolution |
|---|---|---|---|
| 1:1 | Square | Instagram photos, profile pictures | 1080×1080 |
| 4:3 | Standard | Old TVs, tablets, photography | 1024×768 |
| 3:2 | Classic Photo | 35mm film, DSLR photos | 1200×800 |
| 16:9 | Widescreen | HD TV, YouTube, monitors | 1920×1080 |
| 16:10 | Wide | Computer monitors, tablets | 1920×1200 |
| 9:16 | Portrait | TikTok, Instagram Stories, Reels | 1080×1920 |
| 21:9 | Ultrawide | Cinema, ultrawide monitors | 2560×1080 |
Ratio to Decimal, Fraction & Percentage Converter
| Ratio | Fraction | Decimal | Percentage |
|---|---|---|---|
| 1:1 | 1/1 | 1.0 | 100% |
| 1:2 | 1/2 | 0.5 | 50% |
| 2:1 | 2/1 | 2.0 | 200% |
| 1:3 | 1/3 | 0.333 | 33.3% |
| 2:3 | 2/3 | 0.667 | 66.7% |
| 3:4 | 3/4 | 0.75 | 75% |
| 4:3 | 4/3 | 1.333 | 133.3% |
| 16:9 | 16/9 | 1.778 | 177.8% |
Frequently Asked Questions About Ratios
What is a ratio?
A ratio is a comparison of two or more numbers that shows their relative sizes. Written as a:b (read 'a to b'), a ratio tells you how much of one thing there is compared to another. For example, a 2:1 flour-to-sugar ratio means 2 cups of flour for every 1 cup of sugar.
How do I simplify a ratio to its simplest form?
Find the GCD (Greatest Common Divisor) of both numbers, then divide both by it. For example, 8:12 — the GCD of 8 and 12 is 4, so 8÷4 = 2 and 12÷4 = 3, giving 2:3 in simplest form. Our Simplify Ratio mode does this instantly.
How do I find a missing value in a proportion?
Use cross-multiplication. If A:B = C:D, then D = (B × C) ÷ A. For example, 2:3 = 8:? → D = (3 × 8) ÷ 2 = 12.
What is a ratio of 3 numbers?
A three-part ratio compares three quantities, like 6:9:15. To simplify, find the GCD of all three numbers and divide each by it. 6:9:15 → GCD=3 → 2:3:5.
What does aspect ratio mean?
An aspect ratio is the proportional relationship between width and height. Common ratios include 16:9 (widescreen TVs), 4:3 (older monitors), and 1:1 (square photos). A 16:9 screen that's 48 inches wide is 27 inches tall (48×9÷16).
How do I convert a ratio to a percentage?
Divide the first number by the second, then multiply by 100. For example, 3:4 = 3÷4 = 0.75 × 100 = 75%. Our Convert Ratio mode shows this instantly.
How do I convert a ratio to a decimal?
Divide the first number by the second. For example, 3:4 → 3 ÷ 4 = 0.75. For a percentage, multiply the decimal by 100: 0.75 × 100 = 75%.
How do I scale a ratio?
Multiply both parts of the ratio by the scale factor. To double a 2:3 ratio, multiply by 2: 2×2 = 4 and 3×2 = 6, giving 4:6. Use the Scale Ratio mode to scale up or down.
What is a ratio vs a fraction?
A ratio (a:b) compares two quantities and has a total of a+b parts. A fraction (a/b) represents one quantity as a part of a whole. 1:2 ratio means one part to two parts (total 3). 1/2 means one out of two (half). They're related but not interchangeable.
What is a good debt-to-income ratio?
Most lenders prefer a debt-to-income (DTI) ratio of 36% or lower. This means your total monthly debt payments should not exceed 36% of your gross monthly income. A DTI of 20% or less is considered excellent.
How do I calculate aspect ratio from width and height?
Divide both dimensions by their GCD. For example, 1920×1080: GCD of 1920 and 1080 is 120. 1920÷120 = 16, 1080÷120 = 9. Aspect ratio: 16:9.
Reviewed by Shahid
Content Reviewer & Calculator SpecialistContent reviewer specializing in marketing, finance, health, and math calculators on GM Calculator.