Geometric Standard Deviation Calculator
Compute the geometric standard deviation and geometric mean of positive data — the multiplicative spread used for growth rates, ratios and log-normal data.
How it works
GSD = exp(√[ Σ(ln xᵢ − ln GM)² ÷ n ]) · GM = exp(mean of ln xᵢ)
The geometric standard deviation is the multiplicative counterpart of the ordinary standard deviation: it is a dimensionless factor, always at least 1, that you multiply and divide the geometric mean by rather than add and subtract. It is the natural spread measure for data that grow multiplicatively or follow a log-normal distribution — investment returns, particle sizes, concentrations — where a fixed percentage change matters more than a fixed absolute change.
Worked example
For 1.2, 1.5, 0.8, 2.0, 1.1, 1.7 the mean of the natural logs is about 0.246, so the geometric mean is e^0.246 ≈ 1.28. The SD of the logs is about 0.32, so the GSD is e^0.32 ≈ 1.38 — one "geometric SD" band runs from 1.28 ÷ 1.38 ≈ 0.93 to 1.28 × 1.38 ≈ 1.76.
Frequently asked questions
Why can’t the data include zero or negatives?
The calculation takes the natural logarithm of every value, and the log of zero or a negative number is undefined. The geometric standard deviation only applies to strictly positive data.
How do I read a GSD of 1.5?
It means a typical one-sigma band spans from the geometric mean divided by 1.5 up to the geometric mean multiplied by 1.5. A GSD of 1 would mean all values are identical; larger values mean more multiplicative spread.
Does this use n or n−1 in the denominator?
This calculator uses the population form (divide by n), which is the classic definition of the geometric standard deviation. For a sample-based estimate you would divide the log deviations by n−1 instead, giving a slightly larger value.
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This calculator is for educational purposes. Double-check important results before acting on them.