Geometric Mean Calculator

Your details

Values mode: enter the numbers directly. Growth-rate mode: enter each period's percentage change and the calculator converts each to a growth factor (5 becomes 1.05, -10 becomes 0.90) before computing the mean.
Enter positive numbers separated by commas or spaces. Zeros are handled according to the option below.
A zero collapses the entire product to zero. Ignoring is the safest default. In assay or environmental data, replacing with half the detection limit is a common convention.
Enter a starting value, an ending value, and the number of periods to compute the CAGR, which is the geometric mean of the implied growth factors.
Generate a year-by-year table showing how a starting value grows period by period at the actual rates vs. the computed geometric mean rate.
Geometric mean
8
Arithmetic mean14
Harmonic mean4.571429
Count (n)3
Product of values512
Geometric mean8
Arithmetic mean14
Harmonic mean4.571429

Geometric mean of your 3 values: 8.

  • Across 3 values, the geometric mean is 8.
  • The geometric mean is always less than or equal to the arithmetic mean (AM-GM inequality), with equality only when every value is identical.
  • Here the arithmetic mean is 14. The wider your values spread, the larger the gap between the two means.
  • The harmonic mean is 4.571429. For any positive dataset: HM <= GM <= AM.

Next stepUse the geometric mean whenever your data compounds multiplicatively: growth rates, financial returns, ratios, or index numbers built from ratios.

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