Proportion Calculator

A proportion is a statement that two ratios are equal: a divided by b equals c divided by d. Solving a proportion means finding the one missing value when you know the other three, which is done by cross-multiplication. If you know a, b, and d but need to find c, then because a times d equals b times c, it follows that c equals a times d divided by b. This single algebraic step works in any position: the missing value can be a, b, c, or d, and the same cross-multiplication principle applies every time. Proportions are used constantly in everyday situations. Scaling a recipe up or down, converting between units, reading a map or scale drawing, mixing paint or concrete to a ratio, splitting costs in proportion to usage, and calculating how long a job will take at a given rate are all proportion problems. You enter the proportion in the form a divided by b equals c divided by d, placing a question mark (or leaving the field blank) for the unknown value, and the calculator returns the missing number, the completed proportion, both cross-products, and a verification check confirming that the two cross-products are equal. All four values can be positive or negative decimals; b and d cannot be zero because division by zero is undefined. The proportion must have exactly one missing value. This tool is useful for students, tradespeople working with ratios, cooks scaling recipes, and anyone who regularly works with rates and ratios in their work or study.

Leave exactly one field blank to solve for the unknown. The proportion reads a/b = c/d.

c = 9

missing value

Completed proportion3/4 = 9/12

Cross-product 1 (a×d)36

Cross-product 2 (b×c)36

Cross-products must be equal for a valid proportion. Leave exactly one field blank to solve.

How it works

Cross-multiplication converts the proportion a/b = c/d into a linear equation: a times d = b times c. If one of a, b, c, or d is unknown, that equation is rearranged to isolate it. For example, if c is missing: c = (a times d) divided by b. If b is missing: b = (a times d) divided by c. The same logic applies to any of the four positions. The two cross-products, a times d and b times c, are always displayed so you can verify the proportion is satisfied. When all four values are entered, the calculator checks whether the cross-products match rather than solving for an unknown.

Worked example

Using the defaults a=3, b=4, and d=12, with c left blank, gives the proportion 3/4 = c/12. Cross-multiplication: c = (3 times 12) divided by 4 = 36 divided by 4 = 9. The completed proportion is 3/4 = 9/12. Cross-product 1 is 3 times 12 = 36; cross-product 2 is 4 times 9 = 36. They are equal, confirming the answer.

Related calculators

Percentage Calculator: work out what percentage one number is of another.
Golden Ratio Calculator: split a length in the divine proportion phi.
Absolute Value Calculator: find the modulus of any number or expression.
Percent Error Calculator: measure how close a proportional estimate is to the true value.

Frequently asked questions

What is a proportion?

A proportion is a statement that two ratios are equal: a divided by b equals c divided by d. It means that a and b have the same relationship to each other as c and d. Proportions appear in scale drawings, recipe scaling, unit conversions, probability, and many other practical situations.

How do you solve a proportion for a missing value?

You use cross-multiplication. If a divided by b equals x divided by d, then a times d equals b times x, so x equals a times d divided by b. This works because multiplying both sides of a divided by b equals x divided by d by the product b times d clears both denominators.

What are cross-products and why do they matter?

In a proportion a divided by b equals c divided by d, the cross-products are a times d and b times c. A proportion is valid if and only if the cross-products are equal. Cross-products give you a quick way to verify that a proportion is correct without doing any division.

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