Harmonic Mean

All statistics tools

Calculate the average of rates or ratios effectively.

Data Input

Data Set (Rates or Ratios)

Calculation Results

Harmonic Mean48

Arithmetic Mean50.00Simple Average

Sample Size2Rates Counted

Geometric Mean48.99

About this calculator

Overview

The harmonic mean is the correct way to average rates. While the arithmetic mean is used for totals, the harmonic mean is used when you are interested in the average amount of work done per unit. It is particularly useful in physics and finance for averaging rates like speed or price-to-earnings ratios.

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Pro Tips

Use this for rates like speed, density, or frequency.
Ensure all data points are non-zero, as the reciprocal of zero is undefined.
If your data has positive and negative values, the harmonic mean might not be meaningful.

Fun Facts

"If you drive 60 mph to a destination and 40 mph back, your average speed is NOT 50 mph. It's actually 48 mph! The harmonic mean accounts for the fact that you spent more time driving at the slower speed."
"Electricity students use this to calculate the total resistance of resistors in parallel: 1/R_total = 1/R1 + 1/R2 + ..."
"The harmonic mean is one of the three Pythagorean means, along with arithmetic and geometric means."

Formula: H = n / [ Σ (1/xᵢ) ]