Harmonic Mean Calculator

Harmonic Mean Calculator is a free online tool used to calculate the harmonic mean of numbers.

Harmonic Mean Calculator

Please enter numbers. Numbers separated by commas or new lines:

Eg, What is the harmonic mean for the numbers 2, 4 and 5? Enter 2, 4, 5 into the input box and click Calculate button.

What is harmonic mean?

Harmonic mean is the reciprocal of the average arithmetic mean of the reciprocals of each number in a given set of data.

The formula to calculate the harmonic mean is

Formula of harmonic mean Or in a simpler way

Simple formula of harmonic mean

How to calculate the harmonic mean?

Obviously, to calculate the harmonic mean, several steps are required:

1Calculate the reciprocal of each number.
2Calculate the sum of all reciprocals.
3Divide the total number by the reciprocal sum.

For example, calculate the harmonic mean of data 2, 4 and 5.

First, calculate the reciprocal of each number and add them together.

12 + 14 + 15 = 0.5 + 0.25 + 0.2 = 0.95

If you don’t know how to calculate the sum of the fractions, you can use our Three or More Fractions Calculator to easily calculate the sum of the fractions without any conditions.

Then, Divide the total number by the reciprocal sum. Here, the total number is 3, the reciprocal sum is 0.95.

30.95 = 3.15789

So, the harmonic mean of 2, 4 and 5 is 3.15789.

How to use the harmonic mean calculator

The procedure to use the harmonic mean calculator is as follows:

1Enter numbers in the input box. Separate each number with a comma or newline.
2Click Calculate button to calculate the harmonic mean of input numbers.
3Click the Reset button to start a new calculation.

Solved examples using the harmonic mean calculator

Example 1: What is the harmonic mean for the numbers 5 10 15 20?

Enter 5, 10, 15, 20 into the input box and click Calculate button, as shown in the figure, the harmonic mean of them is 9.6.

415 + 110 + 115 + 120 = 4512 = 9.6

What is the harmonic mean for the numbers 5 10 15 20?

Example 2: What is the harmonic mean of 8 and 12?

Enter 8, 12 into the input box and click Calculate button, as shown in the figure, the harmonic mean of 8 and 12 is 9.6.

218 + 112 = 2524 = 9.6

Harmonic Mean Calculator