Power Mean Calculator
Calculate the generalized power mean (Holder mean) for any power p, unifying harmonic, geometric, arithmetic, and quadratic means.
Enter Values
-3-1 (HM)0 (GM)1 (AM)2 (RMS)3
Examples:
Power Mean (p = 2)
6.633250
Special Cases Comparison:
Minimum (p → -∞):2.0000
Harmonic Mean (p = -1):4.379562
Geometric Mean (p = 0):5.210342
Arithmetic Mean (p = 1):6.000000
Quadratic Mean (p = 2):6.633250
Maximum (p → +∞):10.0000
For positive values, power means are ordered: Min ≤ HM ≤ GM ≤ AM ≤ RMS ≤ Max
Number of Values
5
What is Power Mean?
The power mean (also called generalized mean or Holder mean) is a family of functions that includes many well-known means as special cases. By varying the power parameter p, you can obtain the harmonic mean (p=-1), geometric mean (p=0), arithmetic mean (p=1), quadratic mean (p=2), and even the minimum (p→-∞) or maximum (p→+∞).
Formula
Mp = [(x1^p + x2^p + ... + xn^p) / n]^(1/p)
For p = 0, use the limit: M0 = (x1 × x2 × ... × xn)^(1/n) = Geometric Mean