Proportion Calculator

Solve a : b = c : d for whichever term is missing.

Solve a : b = c : d for whichever term is missing. A proportion holds exactly when its cross products match, which is what cross-multiplication is testing.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Solve for

Value of d

2 : 3 = 8 : 12

d12

Completed proportion2 : 3 = 8 : 12

Cross product a × d24

Cross product b × c24

Scale factor4

A proportion holds exactly when its cross products match, which is what cross-multiplication is testing. Both come to 24 here. The scale factor of 4 is the multiplier taking the first pair to the second — the same idea as a map scale or a recipe scaled up.

How the Proportion Calculator works

A proportion holds exactly when its cross products match, which is what cross-multiplication is testing. This solves for any of the four terms and shows both cross products so the balance is visible rather than asserted.

Also known as: solve for x proportion · cross multiplication calculator · ratio and proportion calculator · direct proportion calculator

Where to go next

The Proportion question rarely arrives on its own. These are the ones that usually come with it:

Ratio Calculator — Simplify a ratio, and see it as shares of the whole.
Inverse Proportion Calculator — When the product stays constant instead of the ratio.
Percentage Change Calculator — Change, and the reverse move needed to undo it.
Percentage Calculator — Every common percentage question in one place.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

How do I solve a proportion?

Cross-multiply and divide. In 2 : 3 = 8 : x, multiply 3 by 8 and divide by 2 to get 12.

Why does cross-multiplication work?

Because a proportion is an equation between two fractions. Multiplying both sides by both denominators clears them, leaving the cross products equal.

What is direct proportion?

A relationship where doubling one quantity doubles the other, so their ratio stays fixed. Recipe scaling and map scales both work this way.

How is this different from inverse proportion?

In direct proportion the ratio is constant; in inverse proportion the product is. Twice the workers halving the time is inverse, not direct.

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The one-line version

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