Harmonic Mean Calculator

Harmonic Mean Calculator calculator can be used to calculate the harmonic mean of a set of numbers. The harmonic mean is a type of average that is particularly useful when dealing with rates or ratios.

Input Parameters

Calculation Results

Calculation Formula

Harmonic Mean = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

Where:
n = number of values
x₁, x₂, ..., xₙ = the values in the dataset

Harmonic Mean Calculator Calculator Usage Guide

Learn how to use the Harmonic Mean Calculator calculator and its working principles

How to Use the Calculator

  1. Enter your numbers in the input field, separated by commas. For example: 4, 8, 16, 32
  2. Click the "Calculate" button to compute the harmonic mean
  3. The result will be displayed in the "Harmonic Mean" field
  4. Click "Reset" to clear all inputs and results

When to Use Harmonic Mean

The harmonic mean is particularly useful in situations where you need to average rates or ratios. It tends to reduce the influence of very high values compared to the arithmetic mean.

Examples of Use Cases

  • Calculating the average speed when distances are traveled at different speeds
  • Calculating the average rate of return for investments
  • Calculating the average flow rate in fluid dynamics

Mathematical Explanation

The harmonic mean (H) of a set of n numbers x₁, x₂, ..., xₙ is calculated as:

H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

This formula ensures that each value has an equal weight in the calculation, regardless of its magnitude.