Harmonic Mean (3 Numbers)

Calculate the harmonic mean of three measurements to analyze rates, densities, or other values expressed per unit. This averaging method gives more weight to smaller numbers, making it perfect for combining speeds over the same distance, fuel efficiencies, or cost ratios.

Ideal for rates such as km/h, L/100 km, or cost per unit
All inputs must be positive and non-zero
Mix and match decimals or whole numbers

Mathematical reference only—review assumptions before applying results to critical decisions.

Examples

  • Travel legs at 45, 55, and 60 mph over equal distances ⇒ Harmonic mean 52.4 mph, reflecting your true average speed
  • Server response times of 120, 145, and 200 ms ⇒ Harmonic mean 151.8 ms, which emphasizes the slowest request
  • Investment expense ratios of 0.40%, 0.65%, and 0.80% ⇒ Harmonic mean 0.58%, useful for blended portfolio costs

FAQ

When should I use the harmonic mean instead of the average?

Use the harmonic mean when averaging values expressed as rates or ratios per unit, such as speed, price per unit, or efficiency metrics.

What happens if one of the numbers is very small?

A very small value pulls the harmonic mean downward, spotlighting the bottleneck—exactly why this mean is favored for rate analysis.

Can I include negative values?

Negative rates rarely make sense in practice, but mathematically they can produce misleading results, so keep inputs positive.

Additional Information

  • Unlike the arithmetic mean, the harmonic mean is dominated by the smallest values, so it highlights bottlenecks in your data.
  • The formula is 3 divided by the sum of the reciprocals: 3 / (1/a + 1/b + 1/c).
  • All inputs must be positive and non-zero—rates of zero would make the reciprocal undefined.

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