HARMEAN function

This article describes the formula syntax and usage of the HARMEAN function in Microsoft Excel.

Description

Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the arithmetic mean of reciprocals.

Syntax

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

The HARMEAN function syntax has the following arguments:

• Number1, number2, ...    Number1 is required, subsequent numbers are optional. 1 to 255 arguments for which you want to calculate the mean. You can also use a single array or a reference to an array instead of arguments separated by commas.

Remarks

• The harmonic mean is always less than the geometric mean, which is always less than the arithmetic mean.

• Arguments can either be numbers or names, arrays, or references that contain numbers.

• Logical values and text representations of numbers that you type directly into the list of arguments are counted.

• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.

• Arguments that are error values or text that cannot be translated into numbers cause errors.

• If any data point ≤ 0, HARMEAN returns the #NUM! error value.

• The equation for the harmonic mean is:

  

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Data
4
5
8
7
11
4
3
Formula	Description	Result
=HARMEAN(A2:A8)	Harmonic mean of the data set in A2:A8.	5.028376