Math

Proportion Calculator (Solve for x)

Enter three known values to find the fourth.

By TheCalcTools Updated Formula checked and tested

Your numbers

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x
x
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Working
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Ratio
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Proportion Calculator (Solve for x) by TheCalcTools

How the Proportion Calculator (Solve for x) works

In a direct proportion both quantities change by the same factor: a/b = c/x, so cross-multiplying gives a × x = b × c and x = b × c ÷ a.

In an inverse proportion one goes up as the other goes down, keeping the product constant: a × b = c × x. Example: 4 workers take 10 days, so 6 workers take 4 × 10 ÷ 6 ≈ 6.67 days.

The formula

Direct: x = bc ÷ a; inverse: x = ab ÷ c

Worked example

Using the default values shown in the calculator:

a4
b10
c6
RelationshipDirect: a/b = c/x
  1. 4/10 = 6/x: x = 10 × 6 ÷ 4 = 15.
  2. Inverse: 4 workers × 10 days = 6 workers × x days gives x = 6.666667.

Result:

x15.0000
Workingx = 10 × 6 ÷ 4 = 15
Ratio1 : 2.5

Frequently asked questions

What is the rule of three?

The traditional name for solving a proportion from three known values, as here.

Sources and further reading

Ratio Simplifier CalculatorSimplify a ratio A : B to its lowest terms Percentage CalculatorChoose the question you want answered, enter two numbers, and get the percentage result… Recipe Scaling CalculatorResize a recipe from one serving count to another Unit Price CalculatorWhich size is cheaper per ounce, gram or sheet? Enter both Golden Ratio Calculator (φ = 1.618…)Enter a length and say which part it is

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