Geometric Mean Calculator

Geometric Mean Formula

The geometric mean is calculated by taking the nth root of the product of n numbers. It's particularly useful for calculating average rates of change or growth rates.

Formula:

Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n)

Steps

How to Calculate Geometric Mean

To calculate the geometric mean, follow these steps:

1
Multiply all the numbers together
2
Count how many numbers are in your dataset
3
Take the nth root of the product

For example, to find the geometric mean of 2, 4, 8:

Example Calculation:

Geometric Mean = (2 × 4 × 8)^(1/3) = 64^(1/3) = 4

Examples

Geometric Mean - Practical Examples

Example 1 Investment Returns

An investment grows by 10%, 20%, and 15% over three years. What is the average annual growth rate?

Geometric Mean = (1.10 × 1.20 × 1.15)^(1/3) = 1.1487 = 14.87%

Example 2 Population Growth

A population grows from 1000 to 1500 over 5 years. What is the average annual growth rate?

Growth Rate = (1500/1000)^(1/5) = 1.0845 = 8.45%

Example 3 Rectangle Dimensions

A rectangle has sides of 4 and 9. What is the side length of a square with the same area?

Geometric Mean = √(4 × 9) = √36 = 6

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