# Excel GEOMEAN Function

The Excel GEOMEAN function returns the geometric mean for a set of numeric values. Geometric mean can be used to calculate average rate of return with variable rates.

**number1**- First value or reference.**number2**- [optional] Second value or reference.

The Excel GEOMEAN function calculates the geometric mean. Geometric mean is the average of a set of products — technically, the nth root of n numbers. The general formula for the geometric mean of n numbers is the nth root of their product. The equation looks like this:

For example, given two numbers, 4 and 9, the long-hand calculation for the geometric mean is 6:

=(4*9)^(1/2) =(36)^(1/2) =6

The GEOMEAN function returns the same result:

=GEOMEAN(4,9) // returns 6

By contrast, the arithmetic mean is 6.5:

=(4+9)/2=6.5

The GEOMEAN function takes multiple arguments in the form *number1*, *number2*, *number3*, etc. up to 255 total. Arguments can be a hardcoded constant, a cell reference, or a range. Often, a single range or array is used instead of multiple arguments, as seen in the example worksheet.

### Examples

In the example shown, GEOMEAN is used to calculate a compound annual growth rate. To do this we use the growth factor values in column D in the GEOMEAN function, then subtract 1. The formula in G7 is:

=GEOMEAN(D6:D10)-1

### Notes

- Arguments can be numbers, names, arrays, or references that contain numbers.
- Empty cells, and cells that contain text or logical values are ignored.
- If any provided values are less than or equal to zero, GEOMEAN returns #NUM!

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