# Harmonic Mean Calculator

A harmonic mean calculator is a calculator that you want to calculate the harmonic mean.

#### Example: Find the harmonic mean of the following data : $$({8, 9, 6, 11, 10, 5})?$$

Given data:

$$({8, 9, 6, 11, 10, 5})$$

$$So\ Hormonic\ Mean=\frac{6}{\frac{1}{8}+\frac{1}{9}+\frac{1}{6}+\frac{1}{11}+\frac{1}{10}+\frac{1}{5}}$$ $$H=\frac{6}{0.7936 }=7.560$$ Harmonic mean(H) = $$7.560$$

#### Formula :

$$H.M of X = X¯ = \frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+……………+\frac{1}{x_{n}}}=\frac{n}{\sum (\frac{1}{x})}$$

Where,
n = Total number of numbers or terms.
x1, x2, x3, …. xn = Individual terms or individual values.

## How to calculate the mean with our calculator?

A harmonic mean calculator is a calculator that you want to calculate harmonic mean this tool will give you the result instantly. If you are wondering what is harmonic means calculator then just keep reading this article. We will let you know all about it how to calculate it by hand manually on your book.

We are also going got explain the relationship between both the arithmetic and harmonic mean with the help of a formula that will be easy for you guys to understand and so you will be able to it manually too in an emergency.

## How to calculate the mean with our calculator?

Let's attempt to find the mean of three, 4, 6, and 12:

• Type the primary value into the primary box: it’s 3 in our case.
• Enter the remaining values within the next three boxes. Eight boxes are available at the start, but you'll enter up to 30 numbers - the boxes will appear as you type.

We see that the mean of three, 4, 6, and 12 is adequate to 4.8.

### Formula to calculate the harmonic mean

Here is the formula to calculate harmonic mean;

H= n1x1+1x2+…+ 1xn=ni=0n1xi

What is the harmonic mean?

The mean is one among the three hottest sorts of average, alongside the well-known first moment and therefore the mean.

How to find the harmonic mean?

• Let’s just Count the numbers - for instance there are n of them.
• Compute the reciprocal of every number - recall the reciprocal of x is simply 1/x.
• Add those reciprocals and denote the sum by s.
• Calculate the mean by dividing n by s.
• As an example, allow us to calculate the harmonic average of three , 4, and 6:

There are three numbers, so n = 3

• Let's take the reciprocals: ⅓, ¼, and ⅙
• Hence, we've s = ⅓ + ¼ + ⅙ = ¾.
• Finally, calculate the harmonic average: n / s = 3 / ¾ = 4

### Harmonic average of two and three

• Two Number Harmonic average

We have two positive number and such as x and y. her the harmonic mean formula is simplify to the following numbers,

H = 2 * x * y / (x + y),

So as based on the formula we have to double the x and y and it will be divided by the sum of x and y,

Such as let’s suppose we have the value of x=2  and y-=8.

Now,

H= 2*2*8/(2+8) = 32/10 = 3.2

• Three numbers Harmonic average

in this case we have 3 positive numbers such as x, y, and z. and we have thses following harmonic mean formula:

H = 3 * x * y * z / (x * y + y * z + z * x)

Now lets see by putting value in it.

So the value of harmonic mean of x = 2, y = 5, and z = 10:

H = 3 * 2 * 5 * 10 / (2 * 5 + 5 * 10 + 10 * 2) = 300 / 80 = 15 / 4 = 3.75

### How to use this tool harmonic mean

This harmonic mean calculator is free and web based tool that is really easy to use. This tool is available all over the world you can you it from any country or people from any country can use it.

You have to put all the number in the box we have provided and you will be able to calculate it. You Don’t have to use any formula here and you also don’t have to worry about anything else.

What you have to do is you have to come here simply and you will be able to do the calculation by just putting the right number in it.

Note: bookmark this number so that you can use it on Facebook.

### Q. How To Use This Calculator

A. This Calculator Will Calculate The Harmonic Mean Of A Set Of Numbers.