Ratio Calculator
Three tools for two-term ratios: reduce A:B to lowest terms with the GCD, scale it by any multiplier to get equivalent ratios, or solve A:B = C:x for the missing value by cross-multiplying. Each answer shows the arithmetic. Free, no sign-up.
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
How to Use the Ratio Calculator
- 1. To simplify, use the first section. Enter two positive whole numbers as A and B. The result is the ratio in lowest terms, with the GCD and both divisions shown.
- 2. To scale, use the second section. Enter A, B and a multiplier k. You get A × k : B × k, plus a table of the same ratio multiplied by 2, 3, 4 and 10.
- 3. To find a missing term, use the third section. Enter A, B and C for the proportion A:B = C:x, and the tool solves for x.
- 4. Check the inputs. Simplifying needs whole numbers; the other two sections accept positive decimals.
The Three Operations
| Operation | Method | Example |
|---|---|---|
| Simplify A:B | Divide both by GCD(A, B) | 12:18, GCD 6, becomes 2:3 |
| Equivalent ratio | Multiply both by the same k | 2:3 × 5 = 10:15 |
| Solve A:B = C:x | Cross-multiply: A × x = B × C, so x = B × C ÷ A | 2:3 = 8:x gives x = 3 × 8 ÷ 2 = 12 |
A ratio compares two quantities by division, so multiplying or dividing both sides by the same non-zero number never changes it. That is why 2:3, 4:6 and 20:30 are equivalent, and why simplifying uses the greatest common divisor: it is the largest number that divides both terms exactly, so the result has no common factor left.
Using Proportions
Solving a proportion means finding the term that keeps two ratios equal. Place the known pair first (A:B) and the new known value third (C), and the tool returns x. Typical uses are screen sizes, scale models and recipes.
| Problem | Proportion | Answer |
|---|---|---|
| A 16:9 screen is 1920 pixels wide. How tall is it? | 16:9 = 1920:x | x = 1080 |
| A 4:3 image is 800 pixels wide. How tall is it? | 4:3 = 800:x | x = 600 |
| A recipe uses 2 cups of flour for 3 cups of water. How much water for 8 cups of flour? | 2:3 = 8:x | x = 12 |
| A mix is 5 parts concentrate to 2 parts water. How much water for 35 of concentrate? | 5:2 = 35:x | x = 14 |
Ratios, Fractions and Percentages
A ratio like 2:3 compares one part with another. The whole is 2 + 3 = 5 parts, so the first part is 2/5 (40%) of the total and the second is 3/5 (60%). To share 120 in the ratio 2:3, work out one part (120 ÷ 5 = 24) and multiply: 48 and 72. The calculator handles two-term ratios only, so for a three-part ratio such as 2:3:5, divide each term by the GCD of all three yourself. Convert the parts to fractions with the Fraction Calculator, or to percentages with the Percentage Calculator.
Ratios with decimals
The simplify section needs whole numbers. To simplify 1.5:2, multiply both sides by 10 to clear the decimal point, giving 15:20, which reduces to 3:4. The proportion and equivalent-ratio sections accept decimals directly.
Which Tool Do You Need?
| You want to… | Use |
|---|---|
| Simplify a ratio, scale it, or solve for a missing term | This calculator |
| Add, subtract, multiply or divide fractions | Fraction Calculator |
| Turn a fraction or decimal into the other | Decimal to Fraction Converter |
| Find a percent of a number or a percent change | Percentage Calculator |
| Convert a map scale to real distance | Map Scale Calculator |
Frequently Asked Questions
- How do I simplify a ratio?
- Find the greatest common divisor of both numbers and divide each side by it. 12:18 has a GCD of 6, so it simplifies to 2:3. The first section of the calculator shows the GCD and each division.
- What is an equivalent ratio?
- A ratio that expresses the same relationship after both sides are multiplied or divided by the same number. 2:3, 4:6, 10:15 and 20:30 are all equivalent. The scaling section lists the results for ×2, ×3, ×4 and ×10.
- How do I solve a proportion like A:B = C:x?
- Cross-multiply: A × x = B × C, so x = (B × C) ÷ A. If 2:3 = 8:x, then x = (3 × 8) ÷ 2 = 12. All three values must be positive.
- Can a ratio contain decimals?
- Yes, but ratios are usually written in 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. Only the simplify section requires whole numbers.
- How do I split an amount in a given ratio?
- Add the ratio's terms to get the number of parts, divide the total by that, and multiply by each term. To split 120 in the ratio 2:3, there are 5 parts of 24 each, so the shares are 48 and 72.
- What is the difference between a ratio and a fraction?
- A ratio compares parts with each other (2:3), while a fraction compares a part with the whole (2/5 of 2 + 3). The ratio 2:3 means the parts are 2/5 and 3/5 of the whole.