Standard Error of the Mean Calculator
Estimate the standard error of a sample mean from sample standard deviation and sample size.
How to use this calculator
- Enter the sample standard deviation and the number of observations in the sample.
- Check that all inputs use the same units, time period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by standard error of mean calculator calculator
SEM = sample standard deviation ÷ square root of sample size.
- SEM = sample standard deviation ÷ square root of sample size.
- The standard error describes sampling variability under the sampling design; it is not the same as the spread of individual observations and cannot fix biased sampling.
- The tool validates entered values and formats results for readability; it does not verify assumptions against external records.
Worked examples
Worked example
A sample standard deviation of 12 from 36 observations.
12 ÷ √36 = 2.
The estimated standard error of the mean is 2 units.
Understanding the result
Estimate the standard error of a sample mean from sample standard deviation and sample size.
The standard error describes sampling variability under the sampling design; it is not the same as the spread of individual observations and cannot fix biased sampling.
Important notes
The standard error describes sampling variability under the sampling design; it is not the same as the spread of individual observations and cannot fix biased sampling.
Treat the result as an estimate based on the entered inputs. For regulated, engineering, employment, tax or business decisions, check applicable official rules, specifications and professional guidance.
Frequently asked questions
Does SEM shrink as sample size grows?
Yes, for the same standard deviation it decreases in proportion to the square root of sample size.
Is SEM the population standard deviation?
No. It estimates variability of a sample mean, not the dispersion of individual values.
How should I use the result?
The standard error describes sampling variability under the sampling design; it is not the same as the spread of individual observations and cannot fix biased sampling.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.