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Averages & Means

Geometric Mean Calculator

Find the real geometric mean of non-negative values with overflow-resistant evaluation.

Averages & Means

Enter non-negative values

Stable log-space method
Enter one ordinary decimal per line. Commas and scientific notation are not accepted.

Geometric mean

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Enter one non-negative value per line.
  2. If any value is zero, the geometric mean is exactly zero.
  3. Otherwise, read whether the result is exact or explicitly approximate.

Calculation method

Average logarithms, then exponentiate

For positive values, the geometric mean is the nth root of their product. Computing the mean of logarithms avoids constructing an enormous or tiny intermediate product.

Worked example

Geometric mean of 1 and 4

The product is 4 and its positive square root is 2.

√(1×4) = 2

Supported inputs

Precision and limits

List size

Enter 1–100 values, one per line.

Decimal size

Each value may contain up to 200 digits and 100 decimal places.

Exactness

Exact rational results are never replaced by a rounded decimal; approximations are labelled.

Real domain

Negative values are rejected. Zero is supported and produces exact zero.

Approximation

General positive results are numerical approximations formatted to 15 significant digits; an identical-input shortcut remains exact.