Standard Error Calculator

Calculate the standard error of a sample mean or sample proportion and inspect sampling precision

Your result will appear here.

About the Standard Error Calculator

Standard Error Calculator estimates how much a sample statistic, most commonly the sample mean, would vary across repeated samples. It is a measure of sampling precision rather than the spread of individual observations.

Standard error decreases as sample size grows because larger samples generally estimate the population mean more precisely, assuming the underlying variability stays similar.

How to Use the Standard Error Calculator

  1. Enter the sample standard deviation or population standard deviation as required by the selected formula.
  2. Enter the sample size.
  3. Calculate the standard error.
  4. Use the result with a confidence interval or hypothesis test only when the relevant statistical assumptions are appropriate.

How the Calculation Works

For the sample mean, standard error is SE = s/√n when sample standard deviation s is used.

If the population standard deviation σ is known, SE = σ/√n. The square-root relationship means quadrupling sample size halves the standard error, all else equal.

Worked example

Standard Error Calculator Worked Example

Standard deviation 12 with sample size 36

SE = 12/√36 = 12/6 = 2.

Result guide

Understanding Your Standard Error Calculator Result

A smaller standard error means the sample mean is estimated more precisely. It does not mean individual observations are close to the mean; that is described by standard deviation. Standard error also depends on the statistic being estimated. The familiar s/√n formula applies to the sample mean; proportions, regression coefficients and other statistics use different standard-error formulas.

Before you rely on the answer

Assumptions and Limitations

  • Sample size is positive.
  • Standard deviation is estimated appropriately.
  • The sample and statistic meet the assumptions required for the intended inference.

Practical tip

Using This Result in Practice

Do not report standard error in place of standard deviation when describing data variability. The two answer different questions.

Related calculations

Useful Calculations to Continue With

If you need the spread of individual observations, use the Standard Deviation Calculator.

If you want to turn standard error into an interval estimate, use the Confidence Interval Calculator.

Authoritative references

Useful Official Sources

For standards, definitions or real-world guidance related to this calculation, these primary sources may be useful:

Common questions

Standard Error Calculator FAQ

What is standard error?

A measure of the sampling variability of an estimate, such as the sample mean.

How is standard error different from standard deviation?

Standard deviation describes spread in the data; standard error describes precision of a sample statistic.

What happens to standard error when sample size increases?

It decreases in proportion to the square root of sample size, assuming variability stays similar.