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# The Excel HARMEAN Function

HARMONIC MEAN

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 geometric mean of a set of values, y_{1}, y_{2}, ..., y_{n}is therefore given by the formula:

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.

Further information can be found on the

Wikipedia Harmonic Mean page

## Basic Description

The Excel HARMEAN function calculates the harmonic mean of a supplied set of values.

The format of the function is:

HARMEAN( number1, [number2], ... )

Where the number arguments are one or more positive numeric values (or arrays of numeric values), for which you want to calculate the harmonic mean.

In current versions of Excel (Excel 2007 and later), the function can accept up to 255 number arguments, but in Excel 2003 the function can only accept up to 30 number arguments. However, each argument can be an array of values or a range of cells, each of which can contain many values.

## Harmean Function Example

| A | B |
---|

1 | 2.5 | =HARMEAN( A1:A5 ) |
---|

2 | 3 | |
---|

3 | 0.5 | |
---|

4 | 1 | |
---|

5 | 3 | |
---|

Cell B1 of the above spreadsheet on the right shows a simple example of the Excel Harmean Function, used to calculate the harmonic mean of the values in cells A1-A5.

In this example, the Harmean function returns the value **1.229508197**.

Further examples of the Excel Harmean function can be found on the Microsoft Office website.

## Harmean Function Errors

If you get an error from the Excel Harmean function this is likely to be one of the following:

Common Errors

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

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