Proportion Calculator
A proportion says two ratios are equal. Leave any one of the four values empty and the calculator cross-multiplies and solves for it.
How it works
How the Proportion Calculator works
the part a result on its own leaves out
Why cross-multiplication works
If a/b = c/d, multiplying both sides by bd clears both denominators and leaves ad = bc. It is not a trick — it is one multiplication applied to both sides, the same move used on any equation.
Where proportions turn up
Scale drawings, unit conversion, recipe scaling, similar triangles, percentage problems and map distances are all one proportion once the quantities are lined up consistently.
Common mistakes
Common mistakes with proportions
the errors that actually show up, not every possible slip
Mixing up the order
If the left side is miles over hours, the right side must be miles over hours too. Flipping one side inverts the answer.
Cross-multiplying an addition
Cross-multiplication works on a/b = c/d. It does not apply to a/b + c/d, which needs a common denominator instead.
Losing the units
The number is only half the answer. A proportion between 3 hours and 180 minutes is only true once both are in the same unit.
Questions
Asked often enough to answer here
answers that change how you work
Which box should I leave empty?
Any one of the four. The calculator detects which is missing and solves for it — leave exactly one empty.
Can a proportion have no answer?
Yes, if solving for it would require dividing by zero. The calculator says so rather than returning infinity.
Is a ratio the same as a fraction?
A part-to-whole ratio is. A part-to-part ratio, like 3 red to 2 blue, is not — writing it as 3/2 means something different.
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