How this ratio calculator works
A ratio compares two quantities of the same kind — written with a colon, such as 3:4, and read as "three to four". This tool covers the three things people most often need to do with ratios: solve a proportion for a missing value, simplify a ratio to its lowest terms, and scale a ratio up or down.
A proportion is a statement that two ratios are equal, A:B = C:D. Whenever three of the four values are known, the fourth follows from cross-multiplication: A×D = B×C. Rearranging gives each missing value — for instance D = B×C ÷ A, or A = B×C ÷ D. To simplify, divide both parts by their greatest common divisor (GCD). To scale, multiply or divide both parts by the same number so their relationship is preserved.
Common ratios simplified
| Original ratio | GCD | Simplified | As decimal | As 1 : n |
|---|---|---|---|---|
| 8 : 12 | 4 | 2 : 3 | 0.667 | 1 : 1.5 |
| 10 : 5 | 5 | 2 : 1 | 2 | 1 : 0.5 |
| 9 : 12 | 3 | 3 : 4 | 0.75 | 1 : 1.333 |
| 16 : 9 | 1 | 16 : 9 | 1.778 | 1 : 0.563 |
| 100 : 250 | 50 | 2 : 5 | 0.4 | 1 : 2.5 |
Reference note: decimals are accepted on every field. For decimal inputs the simplifier scales both sides to whole numbers before reducing, and all results are rounded for display while the underlying maths stays exact.
Frequently asked questions
- What is a ratio?
- A ratio compares two quantities of the same kind, showing how much of one there is relative to the other. It is written with a colon, like 3:4, and has no units of its own — it simply expresses relative size.
- How do I solve a proportion?
- A proportion sets two ratios equal, A:B = C:D. Leave exactly one value blank and solve by cross-multiplication: A×D = B×C. In 3:4 = 9:?, the missing D = B×C ÷ A = 4×9 ÷ 3 = 12.
- How do I simplify a ratio?
- Divide both parts by their greatest common divisor. For 8:12 the GCD is 4, so 8:12 simplifies to 2:3. With decimals, scale both sides to whole numbers first, then divide by the GCD.
- How do I scale a ratio up or down?
- Multiply both parts by the same number to scale up, or divide both by the same number to scale down. Scaling 2:3 by 4 gives 8:12. To hit a target on one side, apply the factor that produces it to the other side too.
- What does a ratio like 3:4 mean?
- For every 3 units of the first quantity there are 4 of the second. The whole splits into 3 + 4 = 7 parts, so the first is 3/7 and the second 4/7. As a fraction the ratio is 3/4 = 0.75.
- How do I convert a ratio to a fraction or percentage?
- The ratio A:B as a fraction is A/B. For the first quantity's share of the whole, compute A ÷ (A + B), then multiply by 100 for a percentage. For 3:4 that is 3 ÷ 7 ≈ 0.4286, or about 42.86%.