Proportion Calculator

Proportion Calculator

Enter three known numbers and one unknown (x) to calculate the proportional relationship between two ratios instantly.

Proportion Calculator

Use this proportion calculator to find missing values in proportional relationships. It works using two methods: cross-multiplication and the proportion formula, which express equality between two ratios.

What Is a Proportion?

Definition: When two ratios are set equal to each other, it is called a proportion.

We can write a proportion using either the symbols :: or =. For example:

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

Additional Notes:

Two variables are directly proportional if one variable equals the product of the other and a constant.
Two variables are inversely proportional if the product of the two variables is constant (x · y = constant).

Proportion Formula

The standard formula for a proportion is:

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

How to Solve Proportions

There are two main methods:

Cross Multiplication
Proportion Formula

Example Problem

Solve the proportion 8 : ? :: 6 : 4 for the unknown variable x.

Solution Using Cross Multiplication:

Write the proportion as a fraction: \(\frac{8}{x} = \frac{6}{4}\)
Apply cross multiplication: \(6 \cdot x = 8 \cdot 4\)
Solve for x: \(6x = 32 \Rightarrow x = \frac{32}{6} = \frac{16}{3} \approx 5.33\)

Solution Using the Proportion Formula:

Start with the formula: \(\frac{a}{b} = \frac{c}{d}\)
Substitute known values: \(\frac{8}{x} = \frac{6}{4} = 1.5\)
Solve for x: \(x = \frac{8}{1.5} \approx 5.33\)

Both methods give the same result: x ≈ 5.33.

For more complex problems, you can use the Proportion Calculator to get instant solutions.

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EN	PL	ID
DE	JA	PT
ES	IT	RU
FI

Proportion Calculator