What is a proportion?

A proportion says two ratios are equal: a/b = c/d. Three known values pin down the fourth — which is what makes proportions useful for scaling recipes, maps, prices and similar figures.

How does cross-multiplication work?

Multiplying both sides of a/b = c/d by b × d cancels the denominators and leaves a × d = b × c. The two “cross” products are equal, and from there it is one division to the unknown.

Which box should I leave empty?

Whichever value you do not know. The calculator detects the empty box automatically and solves for it, labelling it x.

Does it work with decimals?

Yes — the cross-multiplication algebra is identical for decimals and negatives.

Fractions & Ratios

Proportion Calculator

Fill in any three boxes of a proportion and the fourth is solved by cross-multiplication — with each algebraic move written out.

Your numbers

A — top left

B — bottom left

C — top right

D — bottom right (leave empty to solve)

Worked solution

x (box D)

3/4 = 9/x — both ratios are 0.75

Cross-multiplying turns the proportion into a plain equation: 3 × 12 = 4 × 9. Solving it gives x = 12.

The working

3 steps

Write the proportion
Two ratios are equal. The unknown sits in the D box.
3/4 = 9/x
Cross-multiply
Multiply each numerator by the other fraction's denominator — the two products must be equal.
3 × x = 4 × 9
Isolate x
Divide both sides by the number multiplying x.
x = 36 ÷ 3 = 12
Box D (x)
12
Both ratios equal
0.75

Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.

The classic use: scaling

If 3 eggs serve 4 people, how many serve 12? Set up 3/4 = x/12, cross-multiply to 4x = 36, divide to get x = 9. Any “this many for that many” question is a proportion — the unknown can sit in any of the four boxes.