Ratio Calculator
Enter the first ratio, a : b.
Work with ratios in three ways: simplify a ratio to its lowest form (12:18 becomes 2:3), scale a ratio to a target total (2:3 over 50 becomes 20:30), and solve an unknown in a proportion (if 3:5 = x:20, x = 12). Useful for recipes, map scales, aspect ratios and mixing concentrates.
How to use the ratio calculator
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1
Pick the mode
Simplify, scale to total, or solve for unknown.
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2
Enter values
For simplify: both sides of the ratio. For scale: ratio + target total. For solve: A:B and C:? (one slot empty).
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3
Read the result
Simplified ratio shows the GCD-divided form. Scaled ratio sums to your target. Solved ratio fills in the missing value.
Three common ratio problems
| Problem type | Example | Answer |
|---|---|---|
| Simplify | 24:36 | 2:3 |
| Scale | Split 120 in 5:3 | 75:45 |
| Proportion | If 3:5 = x:25, find x | 15 |
Under the hood
- Simplify: divide both sides by their GCD. GCD(24, 36) = 12, so 24:36 = 2:3.
- Scale: sum the parts (5 + 3 = 8), divide target by sum (120 / 8 = 15 per part), multiply out.
- Proportion: cross-multiply and solve. A:B = X:C becomes A * C = B * X, so X = A * C / B.
When ratios show up
- Recipes: “2 parts flour to 1 part water” scales up with the ratio calculator. A recipe for 4 people becomes one for 11 by scaling.
- Maps: “1:50,000” means 1 cm on the map is 50,000 cm (500 m) in reality.
- Aspect ratios: 16:9, 4:3, 21:9 describe width-to-height proportions on screens.
- Chemical mixing: “dilute 1:10” means 1 part concentrate, 10 parts water (11 parts total).
Watch the “X to Y” vs “X in Y” trap
“1 to 10” and “1 in 10” mean different things. “Dilute 1 to 10” often means 1 part concentrate + 10 parts water (1:10 ratio, 1/11 concentrate). “1 in 10” means 1 part in 10 total (1/10 concentrate, 9 parts water). Check your context before committing.
Frequently Asked Questions
A ratio compares two quantities (3:5 = 3 boys to 5 girls). A fraction expresses a part of a whole (3/8 of students are boys, if the total is 8). The same underlying numbers, different framings.
Yes, for simplify and scale (e.g. 2:3:5 over 100 = 20:30:50). Proportions with three unknowns are not supported in this tool — use a linear-equation solver for that.
Yes. The calculator will simplify 1.5:2.5 to 3:5 by finding a common multiplier to clear the decimals first.
Sum the parts (4 + 3 = 7), then divide each part by the total. 4/7 = 57.1%, 3/7 = 42.9%. The calculator shows percentages in the scale output.