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Proportion Calculator

Solve a proportion of the form a/b = c/d for whichever value you leave blank, using cross-multiplication — instantly and entirely in your browser.

Leave exactly one box empty and it will be solved.

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=
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Solved value of c
15

By cross-multiplication: a · d = b · c.

Quick answer

A proportion states that two ratios are equal: a/b = c/d. To solve for a missing term, cross-multiply so that a × d = b × c, then divide. For 3/4 = x/20, x = 3 × 20 ÷ 4 = 15. This calculator solves for whichever of the four boxes you leave empty.

Formula & method

Two equal ratios satisfy the cross-multiplication identity a × d = b × c. Leaving one of the four values blank, the tool rearranges this identity to isolate the unknown — for example x = b × c ÷ a when the third term is missing — and divides to find it.

Examples

Example 1: Solve for the third term
Input
3/4 = x/20
Result
x = 15
Why
Cross-multiply: x = 3 × 20 ÷ 4 = 15.
Example 2: Solve for the denominator
Input
2/5 = 8/x
Result
x = 20
Why
x = 5 × 8 ÷ 2 = 20.
Example 3: Solve for the first term
Input
a/6 = 3/9
Result
a = 2
Why
a = 6 × 3 ÷ 9 = 2.

When to use this tool

  • Scaling quantities in recipes, maps, or models that keep the same proportion.
  • Converting between units that have a fixed ratio.
  • Solving similar-triangle and similar-figure side lengths.

Common mistakes

  • Leaving more than one box blank — a single proportion can only solve for one unknown at a time.
  • Multiplying straight across (a × c) instead of cross-multiplying (a × d = b × c).
  • Creating a division by zero by leaving a 0 opposite the unknown.

Frequently asked questions

What is a proportion?

A statement that two ratios are equal, written a/b = c/d. If three of the four numbers are known, the fourth can be found by cross-multiplication.

How does cross-multiplication work?

For a/b = c/d, the products of the diagonals are equal: a × d = b × c. Rearranging this equation isolates whichever term is unknown.

Which box do I leave empty?

Leave exactly one of the four boxes blank. The tool detects it and solves for that value.

Can the answer be a decimal?

Yes. If the numbers do not divide evenly, the result is shown as a decimal, e.g. 1/3 = x/10 gives x ≈ 3.333.

Why does it say it can't be solved?

That happens when the position opposite the unknown is 0, which would require dividing by zero.

Is this the same as a ratio calculator?

Related. A ratio calculator simplifies a single ratio; a proportion calculator solves for a missing term across two equal ratios.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

  • ✓ Free to use
  • ✓ No sign-up required
  • ✓ Runs entirely in your browser — nothing is uploaded.
  • ✓ Formula and method shown above
Last updated: How we calculateReport a correctionDisclaimer

Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.

Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.

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