Solve a proportion A:B = C:D for the missing value.
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How do you solve a proportion A:B = C:D for the missing value?
In a proportion A:B = C:D, the cross products are equal: A × D = B × C. The missing term is found by rearranging this equation. Leave exactly one field blank so the tool knows what to solve for. For example, 1:2 = 5:? solves to 10, because 1 × ? = 2 × 5.
Understanding your result
Leave one and only one field empty so the tool knows what to solve for.
Formula and method
In a proportion A:B = C:D, the cross products are equal: A × D = B × C. The missing value is found by rearranging.
Assumptions and limitations
It solves a single proportion for exactly one missing term, so you must leave one and only one field blank. It assumes the two ratios are genuinely equal (a direct proportion) and does not handle inverse proportions or ratios with more than four parts.
Worked example
1:2 = 5:? solves to 10, because 1 × ? = 2 × 5.
How to use this tool
- Fill in three of the four values.
- Leave the unknown blank.
- Press Solve.
Common mistakes to avoid
- Leaving more than one field blank.
About the Ratio Calculator
Solve a proportion of the form A:B = C:D by leaving exactly one field blank.
Who should use this tool
Cooks adjusting ingredient proportions, students tackling proportion questions, model-makers and mapmakers scaling dimensions, and mixers of paints or chemicals who know three parts of a ratio A:B = C:D and need the fourth value worked out reliably.
Benefits
- Solves any missing term in a four-part proportion instantly
- Uses cross-multiplication so the result is mathematically exact
- Removes guesswork when scaling recipes, mixes or drawings
- Works entirely in your browser with nothing to install
Practical use cases
- Scaling a recipe from four servings up to ten
- Finding a real distance from a map scale ratio
- Mixing paint or resin to a fixed part-to-part ratio
- Solving a proportion word problem for a class
Frequently asked questions
Can it simplify a ratio?
Yes. Enter just A and B to see the simplified ratio.
How does cross-multiplication find the missing value?
In A:B = C:D the cross products are equal, so A times D equals B times C. To find a blank term, rearrange that equation. For 1:2 = 5:?, multiply 2 by 5 and divide by 1, giving 10. The tool performs this rearrangement for whichever field you leave empty.
What happens if I leave more than one field blank?
The tool cannot solve it, because a proportion with two unknowns has infinitely many solutions. You must supply exactly three of the four values and leave a single field empty so there is one clear answer to calculate.