Standard Error Calculator
Calculate the standard error of the mean from sample data.
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Enter the sample standard deviation and sample size. The calculator computes SE = s / sqrt(n). Alternatively, enter raw data in the standard deviation calculator first, then use those results here.
About This Calculator
The standard error of the mean (SEM) measures the precision of the sample mean as an estimate of the population mean. It equals the standard deviation divided by the square root of the sample size. Unlike standard deviation (which measures data spread), standard error measures how much the sample mean would vary across repeated samples.
Frequently Asked Questions
What is the difference between standard deviation and standard error?
Standard deviation measures how spread out individual data points are. Standard error measures how precisely the sample mean estimates the population mean. SE is always smaller than SD (SE = SD / sqrt(n)).
How does sample size affect standard error?
Standard error decreases with the square root of sample size. Quadrupling the sample size halves the standard error.
When do I report SD vs SE?
Report SD when describing the variability in your data. Report SE when describing the precision of your estimate (e.g., in confidence intervals).