Proportion Calculator

Solve proportions and ratios — find the missing value in A/B = C/D.

Enter any three values and leave one field empty — the missing value will be solved automatically using cross-multiplication.

Solved for D:12

3 / 4 = 9 / 12

3 : 4 = 9 : 12

Solving proportions with cross-multiplication

A proportion states that two ratios are equal: A/B = C/D. To find a missing value, cross-multiply: A × D = B × C. Rearranging for the unknown gives: A = B×C/D, B = A×D/C, C = A×D/B, or D = B×C/A. Proportions are used in scaling recipes, maps, unit conversions, similar triangles, and currency exchange. Leave any single field blank and this calculator finds the missing value instantly — all math runs locally in your browser.

Built and maintained by Meet Shah · Last updated 13 August 2026

What this tool is used for

Solving for a missing value in a proportion.
Scaling a recipe or a mixture up or down.
Converting between two ratios expressed in different units.
Working out a scale drawing's real dimension.
Scaling a mixture where only one component's quantity is known.

Frequently Asked Questions

How does cross-multiplication solve for the missing value?: A/B = C/D rearranges to A × D = B × C, and every unknown follows from that one identity: A = B×C/D, B = A×D/C, C = A×D/B, D = B×C/A. It is just multiplying both sides by both denominators, which is why it only works while those denominators are non-zero.
Why does it refuse a zero in B or D?: Because A/B = C/D with a zero denominator is undefined, whichever field you asked it to solve. Cross-multiplying hides that — 3/0 = 9/0 satisfies A×D = B×C perfectly well while meaning nothing — so both denominators of the finished proportion are checked, not only the divisor used along the way.
Can I solve for two unknowns at once?: No, and no tool can. One equation determines exactly one unknown; leave two blank and infinitely many pairs satisfy it. That is why the calculator insists on exactly one empty field rather than trying to guess which answer you wanted.
What is the difference between a ratio and a proportion?: A ratio compares two quantities, 3 : 4. A proportion asserts that two ratios are equal, 3 : 4 = 9 : 12 — it is a statement that can be true or false, where a ratio is just a pair. Scaling a recipe, reading a map, or resizing an image at a fixed aspect are all proportions.
Why are results shown to eight decimals?: Because proportions frequently produce non-terminating decimals — 1/3 of anything — and truncating early compounds when the answer feeds another calculation. Eight places is past the precision of any physical measurement while still short enough to read, and trailing zeros are dropped.

Common errors and gotchas

Cross-multiplying in the wrong order, which inverts the answer.
Assuming a relationship is proportional when it is not, such as area against a linear dimension.
Mixing units between the two ratios, which the cross-multiplication then hides.
Confusing a ratio with a fraction of the whole, where 1:3 is a quarter rather than a third.
Rounding an intermediate value, which the multiplication then magnifies.