Here is a *geometric mean calculator* or geometric average calculator, which will calculate the geometric mean of a list of numbers you input.

Enter any numbers – including decimals, and fractions – and the tool will return the average.

## Geometric Mean Calculator

**Table of Contents**show ▼

## What is the Geometric Average or Geometric Mean?

The geometric mean or average of a set of numbers is a number which represents or describes the central tendency by taking the nth root of the product of n numbers. The geometric mean only works for positive numbers.

In general, an *average* (or *mean*) of a list of numbers is one number that represents or summarizes the whole set. The most common average is the arithmetic mean – a number we get by adding numbers together and dividing by the length of our number list.

The geometric mean is useful when comparing values of different weights, or – as in investment returns – averaging across rates or returns. For more on working with percentage returns, see the worked geometric mean example below.

## Formula for Geometric Mean

The formula for the geometric mean is:

In the formula:

- n: The number of numbers you are averaging together (that is, the length of the list)
- x_1, x_2, etc.: The terms/numbers

### Example Geometric Mean Calculation

The geometric mean is very useful in investing. While your first instinct may be to reach for the arithmetic mean, there are some major downfalls.

Imagine a stock which returns the following over 3 years: -50%, +30%, +20%. What's your average annual return?

(Note we converted .92051 to a negative percentage here by subtracting 1 or 100%, then multiplying by 100)

If you entered those numbers into the arithmetic average, you'd get the wrong answer:

Using the wrong average showed no change – an average 0% return a year. Of course, for every $100 you invested you now have $78... proving you should pick the correct mean.

## Using the Geometric Average Calculator

In the text box at the top, enter a list of numbers to average. As noted, you can toggle between **Numbers** and **Percentages**. If you use **Percentages**, merely put the percentages in (such as -30, 50, etc.) and the tool will convert them to numbers for you.

You could alternatively rewrite your percentages as numbers (divide by 100 and add '1').

When happy, simply hit the **Compute Geometric Mean** button below and DQYDJ will find the geometric average.

Next, try the harmonic mean calculator. *Next, visit our other calculators and tools.*