Find the missing value (x) in a proportion. Leave one field empty to solve for it.
Scale a ratio up or down while maintaining the same proportion.
Understanding Ratios
A ratio compares two quantities by showing how many times one value contains or is contained within the other. Written as A:B (read as "A to B"), ratios are fundamental to proportional relationships in math, science, design, and everyday life.
🎨 Design & Media
- 16:9 — Standard widescreen displays
- 4:3 — Classic TV and presentations
- 1:1 — Instagram squares
- φ (1.618:1) — Golden ratio in art
🍳 Cooking & Recipes
Ratios help scale recipes up or down. A 2:1 ratio of flour to sugar means for every 2 cups of flour, use 1 cup of sugar — whether making a small batch or party-sized.
💰 Finance & Business
- P/E Ratio — Price to earnings
- Debt-to-Income — Loan eligibility
- ROI — Return on investment
🔬 Science & Math
Ratios express concentrations, scale models, gear ratios, and unit conversions. The GCD (Greatest Common Divisor) is used to simplify ratios to their lowest terms.
How Ratio Simplification Works
To simplify a ratio, we find the Greatest Common Divisor (GCD) of both numbers and divide each by it.
Ratio Examples with Step-by-Step Solutions
Example 1: Simplify 120:80
- Find the GCD of 120 and 80. Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. GCD = 40.
- Divide both by 40: 120 ÷ 40 = 3, 80 ÷ 40 = 2.
- Simplified ratio: 3:2.
Example 2: Solve the proportion 5:8 = 15:?
- Cross-multiply: 5 × ? = 8 × 15.
- 5 × ? = 120.
- ? = 120 ÷ 5 = 24.
- Verify: 5:8 = 15:24. Both simplify to 5:8. ✓
Example 3: Convert 0.75:1.25 to a simplified ratio
- Multiply both by 100 to remove decimals: 75:125.
- Find GCD(75, 125) = 25.
- Divide both by 25: 75 ÷ 25 = 3, 125 ÷ 25 = 5.
- Simplified ratio: 3:5.
Example 4: Scale 2:3 to make A equal to 500
- Scale factor = 500 ÷ 2 = 250.
- Multiply both parts: 2 × 250 = 500, 3 × 250 = 750.
- Scaled ratio: 500:750 (same proportion as 2:3).
Ratio to Percentage Conversion
To convert a ratio A:B to percentages, divide each part by the total (A + B) and multiply by 100.
| Ratio | Part A | Part B | Common Use |
|---|---|---|---|
| 1:1 | 50% | 50% | Equal split |
| 2:1 | 66.7% | 33.3% | Two-thirds / one-third |
| 3:1 | 75% | 25% | Three-quarters / one-quarter |
| 3:2 | 60% | 40% | 60/40 split |
| 4:1 | 80% | 20% | 80/20 (Pareto principle) |
| 9:1 | 90% | 10% | 90/10 split |
| 16:9 | 64% | 36% | Widescreen width vs height |
Formula: A% = (A ÷ (A + B)) × 100. B% = (B ÷ (A + B)) × 100.
Common Aspect Ratios Reference
Aspect ratios define the proportional relationship between width and height in displays, images, and video.
| Ratio | Decimal | Common Resolution | Used By |
|---|---|---|---|
| 1:1 | 1.0 | 1080×1080 | Instagram posts, profile pictures |
| 4:3 | 1.333 | 1024×768 | Classic TV, iPad, presentations |
| 3:2 | 1.5 | 2160×1440 | 35mm film, DSLR photos, Surface laptops |
| 16:10 | 1.6 | 1920×1200 | MacBook displays, some monitors |
| 16:9 | 1.778 | 1920×1080 | YouTube, Netflix, most TVs and monitors |
| 21:9 | 2.333 | 2560×1080 | Ultrawide monitors, cinematic video |
| 9:16 | 0.5625 | 1080×1920 | TikTok, Instagram Reels, YouTube Shorts |
Common Mistakes
- Confusing ratio order: 3:5 is not the same as 5:3. The order matters — always match the order to the quantities being compared. "3 boys to 5 girls" is 3:5, not 5:3.
- Adding ratios incorrectly: You cannot add ratios directly. 2:3 + 1:4 does not equal 3:7. To combine ratios, you need a common reference point or convert to fractions first.
- Treating ratios as fractions without context: The ratio 3:2 means 3 parts to 2 parts (total 5 parts). As a fraction of the whole, A is 3/5, not 3/2. Confusing part-to-part with part-to-whole is a common error.
- Forgetting units must match: You cannot simplify a ratio of 2 meters to 50 centimeters as 2:50. First convert to the same unit: 200 cm to 50 cm = 200:50 = 4:1.
- Not simplifying fully: 6:9 simplified to 3:4.5 is wrong — you must keep both values as integers. The correct simplification is 6 ÷ 3 = 2 and 9 ÷ 3 = 3, giving 2:3.
- Scaling only one side: When scaling a ratio, you must multiply both values by the same factor. Multiplying only one value changes the proportion entirely.
Frequently Asked Questions
What is a ratio?
A ratio compares two quantities by showing how many times one value contains or is contained within the other. Written as A:B (read as "A to B"), a ratio of 3:2 means for every 3 units of A, there are 2 units of B. Ratios can also be expressed as fractions (3/2) or decimals (1.5).
How do you simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, to simplify 150:210 — the GCD of 150 and 210 is 30. Dividing both by 30 gives 5:7. A ratio is fully simplified when the GCD of both numbers is 1.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios simplify to the same value. If you know three of the four values, you can solve for the missing one using cross-multiplication: A × D = B × C.
How do you solve a proportion for a missing value?
Use cross-multiplication. In the proportion A:B = C:D, the relationship is A × D = B × C. If D is unknown: D = (B × C) ÷ A. For example, if 3:5 = 12:?, then ? = (5 × 12) ÷ 3 = 20.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities (e.g., 3 boys to 2 girls = 3:2). A fraction represents a part of a whole (e.g., 3/5 of the class are boys). The ratio 3:2 corresponds to the fractions 3/5 and 2/5 of the total. Ratios compare parts to parts; fractions compare parts to wholes.
What is the golden ratio?
The golden ratio (φ, phi) is approximately 1.618:1. Two quantities are in the golden ratio when their ratio equals the ratio of their sum to the larger quantity: (A+B)/A = A/B ≈ 1.618. It appears in geometry, art, architecture, nature (spiral shells, flower petals), and is used in design and photography composition (rule of thirds is a simplified approximation).
How do you convert a ratio to a percentage?
Divide each part by the total and multiply by 100. For the ratio 3:2, the total is 5. A = (3/5) × 100 = 60%. B = (2/5) × 100 = 40%.
What does 16:9 ratio mean?
16:9 means for every 16 units of width, there are 9 units of height. It is the standard widescreen aspect ratio used by most monitors, TVs, and video platforms. A 1920×1080 pixel screen is 16:9 because 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9.
How do you scale a ratio?
Multiply both values by the same factor. Scaling 3:5 by a factor of 4 gives 12:20. The proportion stays identical — 12:20 simplifies back to 3:5. This is useful for recipes, model building, map distances, and resizing images while maintaining proportions.
Can ratios have decimals?
Yes. Ratios like 1.5:1 or 2.5:3.7 are valid. To simplify, first convert to integers by multiplying both sides by the same power of 10. For example, 1.5:2.5 becomes 15:25 (× 10), which simplifies to 3:5.
What is the difference between a ratio and a rate?
A ratio compares two quantities of the same kind (e.g., 3 apples to 2 apples). A rate compares two quantities of different kinds (e.g., 60 miles per 1 hour = 60 mph). Rates include units; ratios are unit-free. Both use the same mathematical structure, but rates always involve different units.
Does this ratio calculator store my data?
No. All calculations run entirely in your browser using JavaScript. No data is sent to any server. You can verify this by using the tool offline after the page loads.
Related Tools
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- Aspect Ratio Calculator — calculate and resize dimensions while maintaining aspect ratios
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- GCD & LCM Calculator — find the greatest common divisor and least common multiple
- Decimal to Fraction Converter — convert decimals to simplified fractions
Privacy & Limitations
- Client-side only. No data is sent to any server. No cookies, no tracking. All calculations run in your browser using JavaScript.
- Integer simplification. Decimal ratios are converted to integers by scaling before simplification. Very small decimals (beyond 4 decimal places) may lose precision due to floating-point arithmetic.
- Two-term ratios only. This tool handles A:B ratios. For three-term ratios (A:B:C), simplify each pair separately or use the GCD of all three values.
- No unit handling. This calculator works with numbers only. Ensure both values use the same unit before entering them (e.g., convert meters and centimeters to the same unit first).
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Ratio Calculator FAQ
What is a ratio?
A ratio compares two quantities by showing how many times one value contains or is contained within the other. Written as A:B (read as 'A to B'), a ratio of 3:2 means for every 3 units of A, there are 2 units of B. Ratios can also be expressed as fractions (3/2) or decimals (1.5).
How do you simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, to simplify 150:210 — the GCD of 150 and 210 is 30. Dividing both by 30 gives 5:7. A ratio is fully simplified when the GCD of both numbers is 1.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 2:3 = 4:6 is a proportion. If you know three of the four values, you can solve for the missing one using cross-multiplication: A × D = B × C.
How do you solve a proportion for a missing value?
Use cross-multiplication. In the proportion A:B = C:D, the relationship is A × D = B × C. If D is unknown: D = (B × C) ÷ A. For example, if 3:5 = 12:?, then ? = (5 × 12) ÷ 3 = 20. So 3:5 = 12:20.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities (e.g., 3 boys to 2 girls = 3:2). A fraction represents a part of a whole (e.g., 3/5 of the class are boys). The ratio 3:2 corresponds to the fractions 3/5 and 2/5. They are related but express different things — ratios compare parts to parts, fractions compare parts to wholes.
What is the golden ratio?
The golden ratio (φ, phi) is approximately 1.618:1 (or 1.618033988...). It appears naturally in geometry, art, and nature. Two quantities are in the golden ratio when their ratio equals the ratio of their sum to the larger quantity: (A+B)/A = A/B ≈ 1.618. It is used in design, architecture, and photography composition.
How do you convert a ratio to a percentage?
To convert a ratio A:B to percentages, divide each part by the total (A+B) and multiply by 100. For the ratio 3:2, the total is 5. A's percentage = (3/5) × 100 = 60%. B's percentage = (2/5) × 100 = 40%.
What does 16:9 ratio mean?
The 16:9 ratio means for every 16 units of width, there are 9 units of height. It is the standard widescreen aspect ratio used by most modern monitors, TVs, and video platforms (YouTube, Netflix). A 1920×1080 pixel screen has a 16:9 ratio because 1920÷120 = 16 and 1080÷120 = 9.
How do you scale a ratio?
To scale a ratio, multiply both values by the same factor. For example, scaling 3:5 by a factor of 4 gives 12:20. The proportion remains the same — 12:20 simplifies back to 3:5. This is useful for recipes, model building, map distances, and resizing images while keeping proportions.
What is a 1:1 ratio?
A 1:1 ratio means both quantities are equal. In photography, a 1:1 aspect ratio produces a square image. In mixing, a 1:1 ratio means equal parts of each ingredient. A 1:1 scale model is the same size as the real object.
Can ratios have decimals?
Yes. Ratios like 1.5:1 or 2.5:3.7 are valid. This calculator handles decimal ratios by scaling both numbers to integers before simplifying. For example, 1.5:2.5 becomes 15:25 (multiply by 10), then simplifies to 3:5 using the GCD.
Does this ratio calculator store my data?
No. All calculations run entirely in your browser using JavaScript. No data is sent to any server. You can verify this by using the tool offline after the page loads.