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