Proportion Calculator

Solve a proportion a/b = c/d for whichever value is missing, with every cross-multiplication step shown so you can see exactly how the answer was reached.

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Missing value —

a·d = b·c (cross multiply) 2 3 = 6 9 a/b = c/d

How to Solve a Proportion

Enter three values of a/b = c/d and leave the fourth blank to see it solved.

1

Fill in three of the four values

Type numbers into a, b, c, and d, leaving exactly one field empty — that's the value the calculator will solve for.

2

The calculator cross multiplies

It rewrites a/b = c/d as a x d = b x c, then divides by whichever known value isolates the missing term.

3

Read the result and steps

The missing value appears at the top, and each cross-multiplication step is listed below it. Need to simplify or compare a single ratio instead? The Ratio Calculator handles that.

Frequently Asked Questions

What is a proportion in math?
A proportion is a statement that two ratios are equal, written as a/b = c/d. It says the relationship between a and b is the same as the relationship between c and d. Proportions show up whenever a rate or scale stays constant, like converting units, scaling a recipe, or reading a map: if 2 cups of flour make 3 servings, then 2/3 = c/9 tells you how much flour makes 9 servings.
How do you solve a proportion using cross multiplication?
For a/b = c/d, cross multiply by setting a × d equal to b × c, then divide to isolate the unknown. For example, in 2/3 = c/9, cross multiplying gives 2 × 9 = 3 × c, so 18 = 3c and c = 6. This calculator applies the same cross-multiplication rule automatically to whichever of the four values you leave blank.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, like 2:3, while a proportion is an equation stating that two ratios are equal, like 2/3 = 4/6. In other words, a proportion is two ratios set equal to each other. Use the Ratio Calculator to simplify or compare a single ratio, and this Proportion Calculator when you already have two ratios and need to solve for a missing term.
Can a proportion be solved if more than one value is missing?
A proportion a/b = c/d is a single equation, so it can be solved uniquely only when exactly three of the four values are known. If two or more are missing there are infinitely many pairs that satisfy it, since 2/3 = c/d is true for c = 4 and d = 6 just as much as for c = 6 and d = 9. This calculator therefore requires exactly one blank field and shows a message if zero or more than one field is left empty. Fill in three values and it cross multiplies to find the fourth.

Related Calculators

A proportion is built from two ratios. The Ratio Calculator simplifies or compares a single ratio, the Percentage Calculator expresses the same relationship out of 100, the Interpolation Calculator applies proportional reasoning between two data points, and the Fraction Calculator handles the arithmetic in exact form.