The HARMEAN function returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the arithmetic mean of reciprocals.

### Syntax

=HARMEAN(num_1,[num_2], … )

Note: Beginning with Excel 2007, you can enter up to 255 number arguments to the function. Excel 2003 would only accept up to 30 number arguments.

#### Arguments

Argument | Description |
---|---|

num_1 | The first number, cell reference, or range for which you want the harmonic mean |

[num_2], … | Optional. Additional numbers, cell references or ranges for which you want the harmonic mean, up to a maximum of 255 |

#### Examples

A | B | C | D | E | F | |
---|---|---|---|---|---|---|

1 | Array1 | Array2 | Formula | Result | Notes | |

2 | 8 | 23 | =HARMEAN(A2:A9) | 4.754615 | Harmonic mean of the data set contained in A2:A9 | |

3 | 3 | 20 | =HARMEAN(A2:A9,B2:B5) | 6.355342 | Harmonic mean of the data set contained in A2:A9 and B2:B5 | |

4 | 5 | 15 | ||||

5 | 12 | 22 | ||||

6 | 4 | |||||

7 | 11 | |||||

8 | 2 | |||||

9 | 10 |

#### Common Function Error(s)

Problem | What went wrong |
---|---|

#VALUE! | Occurs if any of the supplied values cannot be interpreted as numeric values |

#NUM! | Occurs if any of the supplied values are negative |

The harmonic mean is a measure of mean that is calculated as the reciprocal of the arithmetic mean of reciprocals. This can only be calculated for positive values.

The harmonic mean (H) of the positive real numbers x_{1}, x_{2}, … x_{n}, is defined as:

Note that the Harmonic mean is always less than or equal to the geometric mean and the geometric mean is always less than or equal to the arithmetic mean.

See Wikipedia for more information on harmonic mean.