Geometric Standard Deviation Calculator

About this calculator

The geometric standard deviation (GSD) is the multiplicative counterpart to the ordinary (additive) standard deviation, used specifically for data that follows a log-normal distribution — data that is skewed and only takes positive values, where ratios between values matter more than raw differences. Instead of adding and subtracting a spread around a mean, GSD multiplies and divides: roughly two-thirds of the data falls between the geometric mean divided by the GSD and the geometric mean multiplied by the GSD.

This measure is standard in fields where quantities are naturally log-normal, such as environmental and industrial hygiene, where airborne particle sizes and chemical exposure levels are almost always reported with a geometric mean and geometric standard deviation rather than an arithmetic one, and in biology and pharmacology when analyzing concentrations or dose-response data that span orders of magnitude.

Enter a set of positive numbers and the calculator computes both the geometric mean and the geometric standard deviation of your data.