🚀 Use the Ratio Calculator Now
Simplify ratios, find missing values, scale proportions — 100% free.
Open Ratio Calculator →What Is a Ratio?
A ratio is a comparison of two or more quantities. Written as a:b, it tells you that for every 'a' units of one thing, there are 'b' units of 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 a Ratio
Example: Simplify 24:16. GCD of 24 and 16 is 8. 24÷8 = 3, 16÷8 = 2. Simplified ratio: 3:2.
How to Solve a Proportion
Example: If 2:3 = 8:x, then 2x = 24, x = 12.
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 do you need?
2:1 = 3:x → 2x = 3 → 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 4 × 50,000 = 200,000 inches = 3.16 miles apart.
🧪 Mixing Ratios
A cleaning concentrate requires a 10:1 water-to-concentrate ratio. To make 1 liter of solution: water = 10/11 × 1000ml = 909ml, concentrate = 1/11 × 1000ml = 91ml.
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 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 our Ratio Calculator for instant simplification and proportion solving