Standard Error Calculator

About this calculator

The standard error of the mean is calculated as SEM = SD / √n, where SD is the sample standard deviation and n is the sample size. It's easy to confuse with standard deviation, but the two answer different questions: standard deviation describes how spread out individual data points are, while SEM estimates how much the sample mean itself would vary if you repeated the sampling — and it shrinks as the sample gets larger, since bigger samples give more stable estimates of the true population mean.

Researchers report SEM to build confidence intervals (mean ± t·SEM or ± z·SEM) and to draw error bars on charts in biology, psychology, medicine, and social science papers. Anywhere a study reports "mean ± SEM" instead of "mean ± SD," it's using this formula to convey precision of the estimate rather than variability of the raw data.