Proportion Calculator

A proportion is a statement that two ratios are equal, written as a / b = c / d. This proportion calculator takes any three of the four terms and solves for the missing one using cross-multiplication, so you can check ratio problems, scale a recipe, or convert a rate without doing the algebra by hand.

How to use this calculator

1. Enter the first ratio’s two terms, a and b.
2. Enter the known term of the second ratio, c.
3. The calculator solves for the missing fourth term, d, so that a / b = c / d.

Worked example

Take the default inputs: a = 2, b = 3, c = 4.

a / b = c / d
2 / 3 = 4 / d

Cross-multiply and solve for d:

d = (b × c) / a
d = (3 × 4) / 2
d = 12 / 2
d = 6

The completed proportion is 2 / 3 = 4 / 6. Both ratios simplify the same way — 2/3 and 4/6 both reduce to about 0.6667 — which confirms the answer is correct. For the full method behind solving for an unknown term this way, see OpenStax’s guide to solving proportions and their applications.

Frequently asked questions

How do I calculate a proportion by hand?

To calculate a proportion, cross-multiply the two ratios (multiply the numerator of one side by the denominator of the other) and divide to isolate the unknown term. This calculator does that same cross-multiplication step automatically.

What is ratio and proportion, and how are they different?

A ratio compares two numbers, like 2 to 3. A proportion is an equation stating that two ratios are equal, like 2 / 3 = 4 / 6. Ratio and proportion problems usually give you three known numbers and ask you to solve for the fourth.

Is this the same as a sample proportion in statistics?

No. This tool solves numeric ratio equations (a / b = c / d), not statistical hypothesis tests. A sample proportion in statistics refers to the share of a sample with a given trait — for example, the fraction of survey respondents who answered “yes” — usually expressed as a fraction or percentage rather than a missing term in a ratio equation.