Statistics Calculators

Standard Error of the Mean Calculator

Calculate the standard error of the mean (SEM) from a dataset — a measure of how precisely the sample mean estimates the true population mean.

Sample mean —

Sample standard deviation —

Standard error of the mean —

Sample size (n) —

About the Standard Error of the Mean Calculator

The standard error of the mean (SEM) measures how much a sample mean is likely to vary from the true population mean, based on the sample's spread and size. It shrinks as sample size grows, reflecting greater precision.

Formula: SEM = s ÷ √n, where s is the sample standard deviation and n is the sample size

SEM is smaller than the standard deviation itself and is the value used to build confidence intervals and perform hypothesis tests on a sample mean — quadrupling your sample size only halves the SEM.