Geometric and Harmonic Mean Calculator
Two averages for values that multiply or that are rates.
Geometric mean
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Values read —
Harmonic mean —
Arithmetic mean —
Reading this —
The formula
geometric mean = (x₁ × x₂ × … × xₙ)^(1/n) harmonic mean = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ)
The geometric mean is worked out through logarithms, so long lists do not overflow.
What to watch out for
Use the geometric mean for growth factors: enter 5% growth as 1.05 and a 5% fall as 0.95. Use the harmonic mean to average rates over equal distances or amounts, such as speeds.
Frequently Asked Questions
What is the average of 10% growth and then 10% decline?
The factors 1.1 and 0.9 have a geometric mean of 0.994987, so the average change per period is a small fall, not zero.
What is the average speed at 30 and then 60 over equal distances?
The harmonic mean, 40, not 45, because more time is spent at the lower speed.