HARMEAN Function

Excel Functions › Statistical

All versions Statistical

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.


Quick answer:
=HARMEAN({4,5,8,7,11,4,3}) harmonic mean ≈ 5.028

Syntax

=HARMEAN(number1, [number2], ...)
ArgumentDescription
number1RequiredThe first number, reference, or array. All values must be greater than zero.
number2, ...OptionalUp 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.

=HARMEAN({4,5,8,7,11,4,3}) // ≈ 5.028
=HARMEAN(2,4) // = 2.667 (harmonic mean of 2 and 4)

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

Live demo

Pick a HARMEAN example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

When should I use HARMEAN instead of AVERAGE?
Use the harmonic mean when averaging rates over a fixed quantity — e.g. the average speed across equal distances, or an average price/earnings ratio. The arithmetic AVERAGE overstates these.
Why does HARMEAN return #NUM!?
Every value must be greater than zero, because the formula sums reciprocals. A zero or negative number in the data causes #NUM!.
How does the harmonic mean compare to the geometric and arithmetic means?
For any positive data set, harmonic mean ≤ geometric mean ≤ arithmetic mean, with equality only when all the values are identical.
Does HARMEAN ignore text and blank cells?
Yes — when pointed at a range it skips empty cells, text, and logical values, just like AVERAGE, and averages only the numeric entries.

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Related functions: GEOMEAN · AVERAGE · MEDIAN · TRIMMEAN · AVEDEV