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Proportion Calculator

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Note: Enter three known values and the variable that you need to find among the proportion between two ratios.

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Proportion Calculator:

Use this proportion calculator to find missing values in proportional relationships. It uses two methods such as cross-multiplication and proportion formula to represent the equality between two ratios.

What Is A Proportion?

“When two ratios are set equal to each other, then it is called a proportion”

The symbol of proportion is ‘::’ and ‘=’.

Two variables are said to be directly proportional if one variable is equal to the product of the other variable and a constant. If the product of the two variables is a constant, then they are said inversely proportional ( x·y is a constant).

What Is The Proportion Formula?

The formula for proportion is stated as:

a:b::c:d=\(\frac{a}{b}=\frac{c}{d}\)

How To Solve Proportions?

There are two main and easiest ways to solve proportions:

  1. Cross Multiplication
  2. Proportion Formula

We have used both in the given example for better understanding:

Example:

The two ratios are 8:?::6:4, solve for the unknown variable x.

Solution:

Using Cross Multiplication:

Step #1: Construct a Proportion

\(\frac{8}{x}=\frac{6}{4}\)

Step 2: Apply Cross Multiplication

\(\ x\ \times\ 6=\ 8\ \times\ 4\)

\(\ 6x= 32\)

\(\ x=\frac{32}{6}\)

\(\ x=\frac{16}{3}= 5.33…\)

Using The Proportion Formula:

a:b::c:d=\(\frac{a}{b}=\frac{c}{d}\)

\(\frac{8}{x}=\frac{6}{4}\)

\(\frac{8}{x}=\ 1.5\)

\(\ x =\frac{8}{1.5} = 5.33..\)

\(\ x = 5.33..\)

In this example, we have found the proportion manually. But for more complex problems, you can use the above proportion calculator.