## Introduction to the Harmonic Mean Calculator:

Harmonic mean calculator is a digital tool used to **find the harmonic average** in a few seconds. It determines the average of the numbers whose values are divided by their sum value that are the reciprocal of each value.

Our harmonic average calculator is valuable for professionals, researchers, and students to solve different kinds of average problems. It provides you with accurate results without involving you in the calculation of Harmonic means problems.

## What is Harmonic Mean?

The harmonic mean is defined as the **reciprocal sum** of each observation that is divided by the total number of observations from the given number set. Thus it is an inverse method of arithmetic mean.

The harmonic mean is one of the complex methods from the Pythagorean theorem to find the average. Its real-life application is mostly in physics to calculate the average velocity, and density of alloys, and electrical resistances, and in finance, it helps to find the price and earnings average ratio.

## Harmonic Mean Formula:

The **harmonic mean formula** is based on the number of observations or the total number but is different from the regular mean formula.

In this formula, all the number of observation sum is written in ratio and n (total number divided by the sum ratio from the given set. The harmonic mean calculator uses the following formula to solve harmonic mean problems,

$$ \bar{x} \;=\; \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \;=\; \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + … + \frac{1}{x_n}} $$

## How to Calculate Harmonic Mean?

Calculating the harmonic mean is a complex process even if you use its formula, it takes time to find solution. Let's see how the harmonic average calculator finds the **harmonic mean** in some steps.

**Step 1**:

Identify all the number of observations in the given set of data.

**Step 2**:

Take the reciprocal of each number of observations separately.

**Step 3**

Then, add all the sum ratio numbers and add these values in the formula.

**Step 4**

Count the total number of observations n from the given data and add the n value.

**Step 5**

After **adding all the values** in the formula, calculate the given values with the help of the harmonic means calculator and you will get the solution of harmonic mean problem.

The harmonic mean calculator finds harmonic mean easily but it's necessary to understand the manual calculations so an example is given below,

### Example:

Find the harmonic mean of the data set (3, 6, 9):

**Solution**:

Here the number of observations are 3, 6, 9.

Take the reciprocal of these observations:

$$ \frac{1}{3}, \frac{1}{6}, \frac{1}{9} $$

Add these reciprocal,

$$ \frac{1}{3} + \frac{1}{6} + \frac{1}{9} \;=\; \frac{11}{18} $$

As you can see n = 3

Apply harmonic mean formula:

$$ Harmonic\; mean \;=\; \frac{\frac{n}{1}}{x_1} + \frac{1}{x_2} + … + \frac{1}{x_n} $$

$$ H.M \;=\; \frac{\frac{3}{18}}{11} $$

$$ \frac{3 \times 11}{18} $$

$$ H.M \;=\; \frac{54}{11} $$

## How to Use Harmonic Mean Calculator?

Harmonic average calculator has a user friendly interface so that you can use it to calculate the average number value. Before calculating harmonic mean this tool, you must follow some simple steps which are:

**Enter your number**for the average numeric value in the input box.- Review your input number values before hitting the calculate button to start the calculation process.
- Click on the “Calculate” button to get the desired result of your given harmonic mean problem.
- If you want to try out our harmonic mean solver first then you can use the load example option.
- Click on the “Recalculate” button to get a new page for solving more number sets.

## Result of Harmonic Means Calculator:

The harmonic mean calculator gives you the **solution** of average problem when you give it an input. It provides you with solutions in detail. It contain as:

**Result option**:

When you click on the result option, it provides you with a solution for harmonic mean problems.

**Possible Step**:

When you click on the possible steps option, it provides you the solution in step with complete detail.

## Advantages of Harmonic Mean Solver:

Harmonic mean calculator gives you **tons of advantages** whenever you use it to calculate numeric average value problems. These advantages are:

- Our tool saves your time and effort from doing complex calculations of harmonic mean value by giviny results in a few seconds.
- Harmonic average calculator is a free-of-cost tool so you can use it to solve average problems.
- It is a versatile tool that allows you to solve the various types of set data.
- You can use this harmonic means calculator for practicing different harmonic mean questions.
- It is a reliable tool that provides accurate solutions whenever you use it for finding the harmonic average.
- It provides a step by step solution with a complete process of harmonic mean so that you get more clarity.