Standard Error Calculator
Find the standard error of the mean (SEM) from a standard deviation and sample size — or paste your raw data and let the tool find both.
Quick answer: The standard error of the mean is SEM = s ÷ √n. For a standard deviation s = 15 from a sample of n = 25, SEM = 15 ÷ √25 = 15 ÷ 5 = 3.
The standard error of the mean estimates how much a sample mean would vary from sample to sample. Unlike the standard deviation, which describes spread among individual values, the standard error describes the precision of the mean itself — which is why it drives confidence intervals and error bars.
The formula
SEM = s ÷ √n
s = sample standard deviation · n = sample size
s = sample standard deviation · n = sample size
Worked example
A sample of 100 measurements has a standard deviation of 20. SEM = 20 ÷ √100 = 20 ÷ 10 = 2.
Frequently asked questions
What is the standard error of the mean?
An estimate of how much the sample mean would fluctuate across repeated samples: SEM = s/√n.
How is standard error different from standard deviation?
Standard deviation measures spread of the data; standard error measures the precision of the mean and gets smaller as n grows.
How do I lower the standard error?
Collect more data. Because of the √n in the denominator, larger samples give a smaller standard error.
Do I use sample or population SD?
Use the sample standard deviation (n − 1) when estimating from a sample, which is the usual case.
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