This online Harmonic Mean Calculator calculates the harmonic mean of a set of positive real numbers. Enter the set of numbers in the input field of the calculator and click the “Calculate” button. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
Harmonic mean formula
In mathematics, the harmonic mean, sometimes referred to as subcontrary mean, of the \(n\) positive real numbers \({ x }_{ 1 },{ x }_{ 2 },…,{ x }_{ n }\) is defined as:
$${\displaystyle H={\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}={\frac {n}{\sum \limits _{i=1}^{n}{\frac {1}{x_{i}}}}}}$$
In certain cases, the harmonic mean provides a better representation of “average”. For example, if for half the distance of a trip a car moves at 30 miles per hour and for the other half of the distance it moves at 60 miles per hour, then the average speed for the trip is given by the harmonic mean of 30 and 60, which is 40 miles per hour. This is exactly the distance divided by the total amount of time spent for the trip. The simple (arithmetic) mean would give us 45 miles per hour. Various applications of the harmonic mean can be found in electricity, finance, geometry and other sciences.
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Check out our other math calculators such as Arithmetic Mean Calculator and Geometric Mean Calculator.