# Geometric Mean Calculator

URL: https://speedycalculator.com/calculators/math/geometric-mean/
Last updated: 2026-10-30

> The geometric mean calculator finds the n-th root of the product of up to 30 positive numbers, and compares it with the arithmetic and harmonic means.

## Inputs

- Values (positive numbers)

## Results

- Geometric mean
- Arithmetic mean
- Harmonic mean
- Number of values

## Formula

```
GM = (x₁ × x₂ × … × xₙ)^(1/n) = exp(mean of ln xᵢ)
```

## Explanation

The geometric mean is the right average for quantities that multiply: growth rates, investment returns, ratios and index numbers. If an investment grows 10% one year and falls 10% the next, the geometric mean growth factor shows the true average change.

### How to use the Geometric Mean Calculator

- Type the numbers separated by commas, spaces or new lines.
- Read the result – it updates as you type.

Results update as you type, and everything is calculated in your browser.

### How it works

To avoid overflow with many large numbers, the calculator averages the logarithms and exponentiates. All values must be positive.

### What each result means

- **Geometric mean** = gmean([Values (positive numbers)])
- **Arithmetic mean** = mean([Values (positive numbers)])
- **Harmonic mean** = hmean([Values (positive numbers)])
- **Number of values** = count([Values (positive numbers)])

## Worked example

Inputs — Values (positive numbers): 1.10, 0.90, 1.25, 1.05.

Results — **Geometric mean = 1.06766161**; Arithmetic mean = 1.075; Harmonic mean = 1.06028152; Number of values = 4.

## Key terms

- **Geometric mean**: The n-th root of the product of n numbers.

## FAQ

**When should I use the geometric mean?**
For averaging rates of growth, ratios or numbers on very different scales.

**Why must the values be positive?**
Roots of negative products are not real, and a zero makes the mean zero.

**How do the three means compare?**
Harmonic ≤ geometric ≤ arithmetic, with equality only when all values are equal.

**How do I average percentage returns?**
Convert them to growth factors (1 + r), take the geometric mean and subtract 1.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Geometric mean](https://mathworld.wolfram.com/GeometricMean.html)