Standard error of the mean calculator
The standard error measures how precisely a sample mean estimates the population mean, and it shrinks as the sample grows.
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How to use it
- Enter data (separate numbers with commas, spaces or new lines).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
SEM = s ÷ √n, where s is the sample standard deviation (dividing by n - 1) and n is the count.
Example
Result: Standard error (SEM): 0.755929; Sample standard deviation: 2.13809; Mean: 5.
Limits and caveats
- Assumes independent, randomly drawn values.
- Do not confuse it with the standard deviation: it describes the precision of the mean, not the spread of values.
Questions about this tool
How is standard error different from standard deviation?
SD describes the spread of individual values; SE describes how much the mean would vary if you sampled again.
How do I use it for a confidence interval?
For large samples a 95% interval is roughly the mean ± 1.96 × SEM. For small samples use the confidence interval calculator with t.
How do I get it in Excel?
Use =STDEV.S(range)/SQRT(COUNT(range)).