Harmonic Mean Calculator
Calculate the harmonic mean, ideal for averaging rates, speeds, ratios, and other quantities where reciprocals are meaningful.
Enter Positive Values
Note: Harmonic mean requires all positive values
Example Data Sets:
Harmonic Mean
59.405941
Arithmetic Mean
66.000000
Geometric Mean
62.582693
Count (n)
5
Sum of Reciprocals
0.084167
AM-GM-HM Inequality:
Harmonic Mean: 59.405941
Geometric Mean: 62.582693
Arithmetic Mean: 66.000000
HM ≤ GM ≤ AM: Verified
What is Harmonic Mean?
The harmonic mean is the reciprocal of the arithmetic mean of reciprocals. It is particularly useful when dealing with rates, ratios, and speeds. For example, if you travel equal distances at different speeds, the harmonic mean gives the correct average speed. It is also used in computing the F1 score in machine learning and averaging P/E ratios in finance.
Formula
HM = n / (1/x1 + 1/x2 + ... + 1/xn)
Or equivalently: HM = n / Sum(1/xi)