Free ratio calculator
Simplify and scale ratios — enter a ratio to see it in lowest terms, as a fraction, and scaled to any target value, updated live, as you type.
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Ratio simplified by GCF. Decimal = a / b.
Results are estimates. Consult a professional.
How the ratio calculator works
A ratio compares two or more quantities of the same kind. Writing a:b (read 'a to b') means for every a units of the first quantity there are b units of the second. Ratios can be scaled up or down by multiplying or dividing both parts by the same non-zero number.
Worked example: scaling a recipe ratio 3:2
A recipe uses a flour-to-sugar ratio of 3:2, giving 3 cups flour and 2 cups sugar for 5 total cups. To double the recipe to 10 cups, multiply both parts of the ratio by 2.
Common ratios in everyday use
Ratios appear constantly in cooking, mixing, and everyday measurement. The table below shows familiar examples along with their decimal equivalents.
| Context | Ratio | Decimal equivalent |
|---|---|---|
| Baking (flour:water) | 2 : 1 | 2.0 |
| Concrete mix (cement:sand:gravel) | 1 : 2 : 3 | — |
| Paint tint (base:tint) | 4 : 1 | 4.0 |
| Bleach solution (water:bleach) | 9 : 1 | 9.0 |
| Map scale (1 cm = 50 km) | 1 : 5,000,000 | — |
| Screen aspect ratio (widescreen) | 16 : 9 | 1.78 |
Source: common industry standards and everyday conventions.
Tips for working with ratios
Keep these habits in mind to avoid the most common ratio mistakes.
- Simplify first — always reduce a ratio to its lowest terms by dividing both sides by their GCD (e.g. 8:6 → 4:3) before scaling.
- Keep units consistent — both quantities must be in the same unit before forming a ratio; convert cm to cm or kg to kg.
- Use cross-multiplication for proportions — if a:b = c:d, then ad = bc; solve for the unknown by isolating it on one side.
- Find the unit ratio — divide both sides so one side equals 1 (e.g. 3:2 → 1.5:1) for easy mental scaling.
- Watch the order — ratio order matters; flour:sugar 3:2 is different from sugar:flour 2:3.
Accuracy and limitations
Ratio calculations are exact when inputs are integers or simple fractions. Decimal inputs may introduce floating-point rounding at the 15th significant digit. Ratios describe relative quantities only — they do not convey the actual size of either quantity without additional information. For three-way or multi-part ratios (a:b:c), the total-parts approach still applies but requires care when converting to individual fractions of a whole.
Key terms
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