About the ratio calculator
This ratio calculator solves proportions of the form A : B = C : D when one value is missing, simplifies a ratio to its lowest terms, and scales a ratio up or down by a factor.
It handles decimals and fractions in the inputs and shows the cross-multiplication used.
Who should use the ratio calculator
- Students solving proportion problems.
- Cooks and makers scaling recipes or mixes.
- Designers and builders keeping aspect ratios or mix ratios consistent.
How to use the ratio calculator: what each input means
- Mode
- Find a missing value, simplify a ratio, or scale a ratio.
- A, B, C, D
- Fill in three of the four values and leave one blank to find it.
- Terms and scale factor
- For simplifying or scaling, enter two or three ratio terms; scaling also takes a factor above zero.
How the ratio calculator works: method and formula
Two ratios are equal when their cross products are equal: A × D = B × C. The missing value is found by rearranging this equation. To simplify a ratio, any decimals or fractions are cleared by multiplying through, then every term is divided by their greatest common factor. Scaling multiplies each term by the factor.
- Proportion
- A ÷ B = C ÷ D ⇒ A × D = B × C
- Solve for D
- D = B × C ÷ A
How to read your ratio calculator result
The headline is the missing term or the simplified ratio. A simplified ratio uses whole numbers with no common factor. For scaling, the new terms keep the same proportion as the originals.
Ratio Calculator worked example
Solve 3 : 4 = 12 : ?, then simplify 12 : 18 : 30.
- Cross-multiply: 3 × D = 4 × 12 = 48, so D = 16.
- For 12 : 18 : 30, the greatest common factor is 6.
- Divide each term by 6 to get 2 : 3 : 5.
3 : 4 = 12 : 16, and 12 : 18 : 30 simplifies to 2 : 3 : 5.
Practical uses of the ratio calculator
- Scaling a recipe from 4 servings to 10.
- Mixing paint, fertiliser or concrete in set proportions.
- Keeping image aspect ratios consistent when resizing.
Assumptions and limitations of this calculator
- Ratio terms must be non-negative, and you must leave exactly one box empty when solving.
- A zero in the denominator position of a proportion cannot be solved.