Geometric Standard Deviation Calculator

How it is calculated

Enter at least two positive numbers separated by commas or spaces; zero, a negative number or text gives no result, because logarithms need positive values. The engine works on natural logarithms: first the mean of the logs, μ = Σ ln(xᵢ) ÷ n, then the variance of the logs, σ² = Σ (ln xᵢ − μ)² ÷ n. The geometric mean is e^μ and the geometric standard deviation is GSD = e^σ. The variance divides by n, not n − 1, so this is the population version; a sample-based GSD of the same data is somewhat larger. A GSD of 1 means all values are equal, and it is always at least 1 because it is a multiplicative factor, not a distance. Results are rounded to two decimals.

Common mistakes

• Including a zero or a negative number. Logarithms are not defined for them, so the tool returns nothing; remove them or check whether the data is really log-normal.
• Typing a decimal comma such as 2,5. Commas separate values here, so it is read as the two numbers 2 and 5 and the geometric mean changes; write 2.5.
• Reading the GSD as an amount to add and subtract. It is a factor: the range is the geometric mean divided and multiplied by it, not shifted by it.
• Expecting a GSD below 1. The value is always at least 1, and exactly 1 only when every value is identical.
• Comparing the result with a sample-based figure from a statistics package. This tool divides by n, so a package that divides by n − 1 will report a slightly larger GSD.