# Documentation/Calc Functions/HARMEAN

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HARMEAN

## Category:

Statistical Analysis

## Summary:

Calculates the harmonic mean of a set of numbers. The harmonic mean is calculated by dividing the number count by the sum of the reciprocals of each number in the set.

## Syntax:

HARMEAN(Number 1 [; Number 2 [; … [; Number 255]]])

## Returns:

Returns a positive real number which is the harmonic mean of the set of numbers.

## Arguments:

Number 1, Number 2, ..., Number 255 are numbers, references to cells or to cell ranges of numbers for which the harmonic mean is to be calculated.

• If any of the arguments contain a value less than or equal to zero then the function returns an error value. However, empty cells and those with non-numeric (except for logical) values are ignored.

## Additional details:

• The formula for HARMEAN is:

where ai are the set of numbers passed as arguments and n is the size of that set. To find the value of n, use the function COUNT(N).

• For more details on the harmonic mean, visit Wikipedia.

## Examples:

Formula Description Returns
=HARMEAN(23.5;46.7;69.5;4.54) The function calculates the harmonic mean of the arguments passed. 24.2580758724851
=HARMEAN(A1:A5) where A1:A5 contains 1,2,3,4,5 respectively The function calculates the harmonic mean of the arguments passed. 2.60517108469735
=HARMEAN(A1:A5) where A1:A5 contains 1,2,-3,4,5 respectively The function returns an error value since one of the arguments passed contains a negative value. Err:502
=HARMEAN(A1:A5) where A1:A5 contains 1,0,3,4,5 respectively The function returns an error value since one of the arguments passed contains 0. Err:502

HARMEAN