Harmonic Mean Calculator

The Harmonic Mean Calculator helps you calculate the harmonic mean of a set of numbers quickly and accurately. Enter your values to get the result instantly, along with useful details such as the number of values, sum, minimum, and maximum. It is especially helpful for understanding averages involving rates, ratios, and other real-world calculations.

Calculate the harmonic mean of a set of numbers instantly. Ideal for rates, ratios, and other numerical data.

Enter Your Numbers Separate values with commas, spaces, semicolons, or line breaks. Every value must be nonzero. Positive values are recommended for conventional rate calculations.

Decimal Places Choose the number of decimal places shown in the result.

Try an example

Choose a sample data set to calculate its harmonic mean.

Calculation Result

Your answer updates automatically as you enter numbers or change the precision.

Harmonic Mean

3.12

Calculation complete.

Calculation details

The harmonic mean is calculated by dividing the number of values by the sum of their reciprocals.

Number of values 4 Sum of values 14 Sum of reciprocals 1.25 Minimum value 2 Maximum value 5

Harmonic mean formula

HM = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ)

4 ÷ (1/2 + 1/3 + 1/4 + 1/5) = 3.12

What Is the Harmonic Mean?

The harmonic mean is a type of average that is particularly useful when working with rates, ratios, and values expressed on a per-unit basis. Unlike the arithmetic mean, it gives more weight to smaller values, making it useful for certain types of calculations involving speed, efficiency, and similar measurements.

Harmonic Mean Formula

The harmonic mean is calculated by dividing the number of values by the sum of their reciprocals.

Harmonic Mean Formula:

\displaystyle H=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}}

Here:

n is the total number of values.
x₁, x₂, … represent the individual values.
Each value must be nonzero, and the sum of the reciprocals must not be zero.

How to Use the Harmonic Mean Calculator

Enter your numbers in the input box.
Separate the values using commas, spaces, semicolons, or new lines.
Choose the number of decimal places you want in the result.
View the calculated harmonic mean and the additional statistics.
Use Clear All to remove the current values or Reload Defaults to restore the default example.

Example of Harmonic Mean

Suppose you want to calculate the harmonic mean of 2, 3, and 6.

Step 1: count the values: n = 3

Step 2: add their reciprocals:

\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}=1

Step 3: Divide the number of values by the reciprocal sum:

\displaystyle H=\text{Harmonic Mean}=\frac{3}{1}=3

Therefore, the harmonic mean of 2, 3, and 6 is 3.

When Is the Harmonic Mean Useful?

The harmonic mean is often used when averaging rates or ratios under suitable conditions. For example, it can help calculate average speed over equal distances when the speeds differ. It is also used in finance, statistics, science, and data analysis when the harmonic mean is appropriate for the data.

Harmonic Mean vs. Arithmetic Mean

The arithmetic mean is calculated by adding all values and dividing by the number of values. The harmonic mean uses the reciprocals of the values instead.

The arithmetic mean is suitable for many everyday averages, while the harmonic mean is often more appropriate for certain rates and ratios. Choosing the right average depends on what the numbers represent and how they relate to one another.

Harmonic Mean Calculator