Free · Sampling and standard errors

Standard Error of the Mean from SD & Sample Size

Calculate the standard deviation of a sample mean from an entered standard deviation and the number of independent observations.

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Enter the known values in the units shown. Results update as you type.
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For SD = 12 and 16 independent observations, the standard error is 12 ÷ √16 = 3 in the same measurement units.

Standard error of mean = standard deviation ÷ √sample size

Enter these known values and leave the other values blank.

Observations are independent with a common variance. Dependence, weighting or sampling without replacement from a small finite population can require another variance formula.
Sample size is a positive whole number. SD and standard error may be zero for zero variability.
Using population SD gives the model standard error; using a sample SD gives an estimate. Estimating sample SD itself requires at least two observations.
A sample size recovered from a target standard error may not be an integer. For a minimum-size planning problem, round up separately and recheck the standard error.

No. SD describes variation among observations; standard error describes variation in the sample mean under the sampling model.

For a fixed SD under this model, the standard error is halved.

Zero variability gives zero standard error and is valid for the stated independent-observation model.