How to use Ratio Calculator
The ratio calculator provides three modes in one tool: simplify a ratio to its lowest terms using the greatest common divisor; scale a ratio by any multiplier; and solve A:B = C:D for any missing term by cross-multiplication. Results are shown instantly with the simplified or scaled ratio or the solved unknown value. Useful for recipes, mixing solutions, map scales, aspect ratios, financial comparisons, and unit conversions.
- Select the mode: Simplify, Scale, or Solve A:B = C:?
- In Simplify mode, enter the two ratio values A and B.
- In Scale mode, enter A, B, and the multiplier to produce a scaled version of the ratio.
- In Solve mode, enter three of the four values (A, B, C, D) and leave the unknown blank.
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How ratio simplification works
A ratio A:B is simplified by dividing both terms by their greatest common divisor (GCD). The GCD is computed using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. For example, GCD(12, 8): 12 mod 8 = 4, 8 mod 4 = 0 → GCD = 4. So 12:8 = (12÷4):(8÷4) = 3:2. A simplified ratio has no common factors other than 1.
| Original ratio | GCD | Simplified |
|---|---|---|
| 10:15 | 5 | 2:3 |
| 12:8 | 4 | 3:2 |
| 100:25 | 25 | 4:1 |
| 7:3 | 1 | 7:3 (already simplified) |
| 360:240 | 120 | 3:2 |
Solving for missing ratio terms
When A:B = C:D, the cross-multiplication rule states A×D = B×C (the product of the means equals the product of the extremes). Given any three values, the fourth is solved by rearranging: D = (B×C)/A; C = (A×D)/B; B = (A×D)/C; A = (B×C)/D. This is used in scaling recipes (if 2 cups flour to 3 cups water makes 1 loaf, how much water for 5 cups flour?), currency conversion, and map scale calculations.
Worked examples
Simplify a ratio
Inputs: 12:8
Result: 3:2 (GCD 4)
Scale a ratio
Inputs: 2:3 × 4
Result: 8:12
Solve for a missing term
Inputs: 3:4 = 9:?
Result: ? = 12
Ratio as fraction and percentage
| Ratio | Fraction of whole | Percentage |
|---|---|---|
| 1:1 | 1/2 | 50% |
| 1:2 | 1/3 | 33.3% |
| 1:3 | 1/4 | 25% |
| 2:3 | 2/5 | 40% |
| 3:1 | 3/4 | 75% |
Glossary
- Ratio
- A comparison of two quantities expressed as A:B or A/B, indicating how many times one contains the other.
- Greatest Common Divisor (GCD)
- The largest positive integer that divides both numbers without a remainder; used to simplify ratios.
- Cross-multiplication
- Multiplying the numerator of one fraction by the denominator of the other to solve proportions: if A/B = C/D then A×D = B×C.
- Aspect ratio
- The ratio of width to height of an image or screen, e.g. 16:9 for widescreen HD displays.
Related reading
Frequently Asked Questions
Why use Ratio Calculator?
- Simplifies any ratio to lowest terms using the exact Euclidean GCD algorithm
- Scales a ratio by any multiplier to produce proportionally correct new values
- Solves A:B = C:D for any single missing term via cross-multiplication in one step
- Three modes in a single tool eliminate the need to switch between different calculators
Common use cases
- Reduce a 360:240 pixel image dimension ratio to its simplest form for responsive CSS
- Scale a concrete-mix ratio from a 4-bag batch to an 11-bag batch without errors
- Find the missing fourth term in a proportion word problem for a maths assignment
- Convert a map scale ratio to a real-world distance using the solve-for-unknown mode
- Verify that two stated aspect ratios are equivalent before cropping a photograph
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