Ratio Calculator
Three ratio tools in one: simplify a ratio to its lowest terms, scale it up or down to find equivalent ratios, and solve proportions with cross-multiplication. Every result shows the working with your numbers.
Simplify a ratio A:B
12 : 18 = 2 : 3
GCD(12, 18) = 6
12 ÷ 6 = 2
18 ÷ 6 = 3
Simplified ratio: 2 : 3
Equivalent ratios — scale A:B by a multiplier
2 : 3 = 10 : 15
2 × 5 = 10
3 × 5 = 15
Both sides multiplied by 5, so the ratio stays the same.
| Multiplier | Equivalent ratio |
|---|---|
| ×2 | 4 : 6 |
| ×3 | 6 : 9 |
| ×4 | 8 : 12 |
| ×10 | 20 : 30 |
Solve a proportion A:B = C:x
x = 12
2 : 3 = 8 : x
Cross-multiply: 2 × x = 3 × 8
2 × x = 24
x = 24 ÷ 2 = 12
Frequently Asked Questions
- How do I simplify a ratio?
- Find the greatest common divisor (GCD) of both numbers and divide each side by it. For example, 12:18 has a GCD of 6, so it simplifies to 2:3.
- What is an equivalent ratio?
- An equivalent ratio is one that expresses the same relationship after multiplying or dividing both sides by the same number. 2:3, 4:6, and 20:30 are all equivalent.
- How do I solve a proportion like A:B = C:x?
- Use cross-multiplication: A × x = B × C, so x = (B × C) ÷ A. For example, if 2:3 = 8:x, then x = (3 × 8) ÷ 2 = 12.
- Can a ratio contain decimals?
- Yes, but ratios are usually written with whole numbers. Multiply both sides by a power of 10 to clear the decimals first — 1.5:2 becomes 15:20, which simplifies to 3:4. The simplify section of this tool works with whole numbers.
- What are ratios used for?
- Ratios compare two quantities: recipe ingredients, map scales, aspect ratios, mixing paint or concrete, and converting between units. Proportions let you scale a known ratio to a new situation.