Ratio Calculator
Simplify ratios, solve proportions and find the scale factor between A:B and C:D.
🔒 Runs entirely in your browser — nothing is uploadedRatio and proportion formula
A ratio compares two quantities, such as 4:6 or 16:9. A proportion says two ratios are equal: A:B = C:D. Written as fractions, that is A/B = C/D. Cross multiplication gives the main formula: A × D = B × C. If one term is missing, the calculator solves that equation. For example, if A, B and C are known, then D = B × C ÷ A. The other missing terms are rearranged the same way.
Simplifying a ratio divides both sides by a common factor while keeping the relationship the same. The ratio 4:6 simplifies to 2:3 because both numbers divide by 2. Decimal ratios are first scaled to whole numbers, so 1.5:2.5 becomes 15:25 and then simplifies to 3:5. This makes the result easier to compare, print or use in recipes, maps, drawings and mixtures.
Scale factor
The scale factor describes how to move from the left ratio to the right ratio. If 4:6 equals 10:15, the scale factor is 2.5 because 4 × 2.5 = 10 and 6 × 2.5 = 15. This is helpful for resizing ingredients, preserving model proportions, expanding a drawing or checking equivalent rates. If the two ratios are not equivalent, the scale factor line explains that the A-to-C and B-to-D multipliers do not match.
Input and privacy notes
Ratios usually need positive values for real-world meaning. The calculator warns when a value needed for division is zero because the missing term would be undefined. It does not upload recipes, dimensions, grades or any other values. All solving and simplification happen in your browser using ordinary JavaScript arithmetic.
Worked examples
Scaling a recipe: if 3 cups of flour go with 2 cups of sugar, set A = 3, B = 2 and C = 4.5, then solve for D. D = 2 × 4.5 ÷ 3 = 3 cups of sugar. Map reading works the same way: at a scale of 1:25,000, set A = 1, B = 25,000 and C = 4 cm to solve for D = 100,000 cm, which is 1 km on the ground.
Keep the units consistent within each side of a ratio, and watch the order, because 3:2 and 2:3 are different ratios. The calculator handles two-term ratios, so for a three-part mix such as 1:2:3, compare two parts at a time. Check any result by cross multiplying: A × D should equal B × C, which is a fast way to catch a mistyped value.
How to use
- Enter a proportionFill A:B = C:D and choose which term, if any, should be solved.
- Simplify ratiosThe calculator reduces both ratios to their simplest integer form when possible.
- Use the scale factorReview how much the left ratio is scaled to match the right ratio.