What is Standard Error?
The standard error of the mean (SEM) estimates how much a sample’s average is likely to differ from the true population average, based on how variable the data is and how large the sample is.
The Formula
SE = standard deviation / √(sample size). As the sample size grows, the standard error shrinks, because larger samples give a more precise estimate of the population mean. This calculator also shows an approximate 95% confidence margin of error, calculated as 1.96 × SE, based on the normal approximation.
- Sample size must be 1 or greater.
- The 95% margin of error assumes a roughly normal sampling distribution, which is a reasonable approximation for most moderately sized samples.
Provided for general statistical education and research planning purposes.
Last reviewed August 2026