Harmonic Mean Calculator

On this page the harmonic mean of a series of numbers is calculated.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button. The list can be entered unsorted.

Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste

The harmonic mean is one of several kinds of average. The harmonic mean can be expressed as the reciprocal of the arithmetic mean and is used around the mean to calculate ratios (quotient of two quantities).

Formulas for the harmonic mean

\(\displaystyle H=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+ ... +\frac{1}{x_n}} = \frac{n}{\sum^n_{i=1}\frac{1}{x_i}} \)

Example

In the following example we calculate the mean of the 5 numbers

\(\displaystyle 5,3,4,2,6 \)

\(\displaystyle H=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}+\frac{1}{x_4} +\frac{1}{x_5}} \)

\(\displaystyle H=\frac{5}{\frac{1}{5}+\frac{1}{3}+\frac{1}{4}+\frac{1}{2}+\frac{1}{6}}≈ 3.45\)

More statistics functions

Arithmetic Mean • Contraharmonic Mean • Covariance • Empirical distribution CDF • Deviation • Five-Number Summary • Geometric Mean • Harmonic Mean • Inverse Empirical distribution CDF • Kurtosis • Log Geometric Mean • Lower Quartile • Median • Pooled Standard Deviation • Pooled Variance • Skewness (Statistische Schiefe) • Upper Quartile • Variance