Harmonic Mean Calculator

Enter value and click on calculate. Result will be displayed.

H.M = n / (1/x1 + 1/x2 + 1/x3 + ... + 1/x2)

Enter Numbers :
Result:
Harmonic Mean :

What is a Harmonic Mean Calculator?

A Harmonic Mean Calculator computes the harmonic mean of a set of numbers, which is the reciprocal of the arithmetic mean of the reciprocals. The formula is:

where:

  • n = total number of values
  • xi​ = each individual value

Why is a Harmonic Mean Calculator Important?

  • Helps in averaging rates (e.g., speed, density, resistances)
  • More accurate for data with large variations
  • Used in finance, physics, and engineering for proportional calculations

How Does It Work?

  1. Take the reciprocal of each number
  2. Find their average
  3. Take the reciprocal of that average to get the harmonic mean

Example: For 3, 4, and 6:

When is a Harmonic Mean Calculator Used?

  • Physics: Calculating average speed when distance is constant
  • Finance: Computing average price-to-earnings ratio (P/E ratio)
  • Statistics: Used in F1-score in machine learning
  • Engineering: Parallel resistance calculations in electrical circuits