Free Harmonic Mean Calculator

Find the harmonic mean of positive values, ideal for averaging rates and ratios.

Harmonic Mean

48.0000

Arithmetic Mean (for comparison)50.0000

Harmonic Mean vs Value 1

How to Compute the Harmonic Mean

Formula (for two values)

Harmonic Mean = 2 / (1/a + 1/b)

More generally for n values: HM = n / (1/v1 + 1/v2 + ... + 1/vn)

The harmonic mean gives more weight to smaller values. It is the correct average to use when the quantities are defined in relation to a common unit, such as speed over the same distance at different rates.

Example Calculation

A car travels 100 km at 40 km/h and returns at 60 km/h. What is the average speed?

  1. 01Reciprocal sum = 1/40 + 1/60 = 0.025 + 0.01667 = 0.04167
  2. 02Harmonic Mean = 2 / 0.04167 = 48
  3. 03The average speed is 48 km/h (not 50 as the arithmetic mean would suggest)

Frequently Asked Questions

Learn More

Understanding the Normal Distribution

Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.

Related Calculators