Standard Error Calculator

About this calculator

The standard error of the mean (SEM) measures how much a sample mean is likely to vary from the true population mean, calculated as the sample standard deviation divided by the square root of the sample size: SEM = SD ÷ √n. Unlike standard deviation, which describes how spread out individual data points are, SEM describes the precision of the mean itself as an estimate, and it shrinks as sample size grows, since larger samples give a more reliable estimate of the true mean.

Researchers report SEM alongside means in scientific papers to communicate how much sampling uncertainty surrounds a result, and it’s the basis for constructing confidence intervals, roughly mean plus or minus 1.96 × SEM for a 95% interval under a normal approximation, and for running significance tests like the t-test that compare sample means. Mixing up SD and SEM is a common statistical error, since SEM will always be smaller than SD for a sample size greater than 1, and reporting the wrong one can make results look more or less precise than they really are.

This calculator takes your sample’s standard deviation and sample size and returns the standard error of the mean.