# Mean Calculator

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

> The mean calculator finds the arithmetic, geometric or harmonic mean of a data set – or all three at once – for numbers separated by commas or spaces.

## Inputs

- Data set
- Type of mean

## Results

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

## Formula

```
Arithmetic A = Σx / n   Geometric G = (Πx)^(1/n)   Harmonic H = n / Σ(1/x)
```

## Explanation

There are several kinds of mean, each suited to different data: the arithmetic mean for ordinary quantities, the geometric mean for growth rates and ratios, and the harmonic mean for rates such as speeds. For positive data, H ≤ G ≤ A.

### How to use the 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

Choose the type of mean. Geometric and harmonic means require positive numbers.

### Inputs explained

FieldWhat to enterData setA list of numbers separated by commas, spaces or new linesType of meanChoose one: Arithmetic, Geometric, Harmonic, All three

### What each result means

- **Arithmetic mean** = mean([Data set])
- **Geometric mean** = gmean([Data set])
- **Harmonic mean** = hmean([Data set])
- **Number of values** = count([Data set])

## Worked example

Inputs — Data set: 4, 8, 15, 16, 23, 42; Type of mean: All three.

Results — **Arithmetic mean = 18**; Geometric mean = 13.96549685; Harmonic mean = 10.49952448; Number of values = 6.

## Key terms

- **Mean**: A central value of a data set.

## FAQ

**What is the mean of 4, 8, 15, 16, 23, 42?**
108 ÷ 6 = 18.

**Which mean should I use?**
Arithmetic for ordinary data, geometric for multiplicative growth, harmonic for rates.

**Why is the geometric mean smaller?**
By the AM–GM inequality, it never exceeds the arithmetic mean.

**Is the mean the same as the average?**
"Average" usually means the arithmetic mean.


## Sources

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