The Excel HARMEAN function returns the harmonic mean of a data set — the reciprocal of the average of reciprocals. It is the right average for rates and ratios such as speed, price/earnings, or parallel resistances.
Syntax
| Argument | Description | |
|---|---|---|
number1 | Required | The first number, reference, or array. All values must be greater than zero. |
number2, ... | Optional | Up to 254 additional numbers or ranges. Empty cells, text, and logical values in a range are ignored. |
How to use it
The harmonic mean is defined as n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ) — the count divided by the sum of the reciprocals.
The harmonic mean is always ≤ the geometric mean ≤ the arithmetic mean. It is the correct average when the values are rates — for example the average speed over equal distances, where a simple AVERAGE would overstate the result.
All values must be positive. Because HARMEAN divides by each value, any zero or negative number returns #NUM!.
Try it: interactive demo
Pick a HARMEAN example to see the formula and its result.
Practice workbook
Frequently asked questions
When should I use HARMEAN instead of AVERAGE?
Why does HARMEAN return #NUM!?
#NUM!.How does the harmonic mean compare to the geometric and arithmetic means?
Does HARMEAN ignore text and blank cells?
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