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Math & Statisticsratio

Proportion Solver

Solve a proportion for its missing fourth term by cross-multiplication. The check is built in: both cross products must be equal, and they are shown.

Also called: cross multiplication calculator, solve for x ratio.

The missing term, d
20

a is to b as c is to d gives d = 20. Cross-multiplying, 3 times 20 equals 4 times 15, both 60.

Both cross products
60
The ratio a to b as a decimal
0.75
The full proportion
3 : 4 = 15 : 20
Scale factor from a to c
5
How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

How this is calculated

A proportion says two ratios are equal. Cross-multiplying turns that statement into an equation with one unknown, which solves in one division. The reason to show both cross products is that they must be identical, so a reader can verify the answer without repeating the arithmetic, which is the whole value of the method.

cross-multiply and solve: d = b * c / a
a
First term, which becomes the divisor
b
Second term
c
Third term
d
The term being solved for

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

three to four as fifteen to twenty

a
3
b
4
c
15

The missing term, d20

Cross products both 60, checked by hand

Open this example

a scale factor of one leaves it unchanged

a
3
b
4
c
3

The missing term, d4

boundary

Open this example

Method and limits

What it assumes

  • The first term is non-zero, since it becomes the divisor.

What it deliberately does not model

  • Direct proportion only. Inverse proportion needs the reciprocal relationship instead.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What if my quantities are inversely related?
Then this is the wrong tool. In inverse proportion the product is constant rather than the ratio, so more workers means less time rather than more.