Standard Error Calculator
The Standard Error Calculator estimates how much the sample mean would vary from sample to sample under a common independent-sampling model. It uses the sample standard deviation and number of observations.
How to use this calculator
- Enter the sample standard deviation and positive sample size from the same sample.
- Review the worked sample size effect and compare its arithmetic with the inputs you plan to use.
- Change one input at a time when exploring a different scenario, and keep units and assumptions consistent.
Standard error of the mean
Standard error = sample standard deviation ÷ square root of sample size.
- With larger samples the standard error of the mean generally shrinks as 1/√n, holding sample variability constant.
- The page's numerical output is calculated from the values entered; it does not independently verify whether those inputs fit the real-world situation.
Worked examples
Sample size effect
If sample standard deviation is 12 and sample size is 36, the standard error is 2.
12 ÷ √36 = 12 ÷ 6 = 2
Estimated standard error is 2 units.
Understanding the result
Standard error describes uncertainty in the estimated mean rather than the spread of individual observations.
The formula may not apply directly to clustered samples, complex surveys, strong dependence, or biased samples.
Important notes
Use the matching sample standard deviation and describe the sampling design when reporting the result.
Displayed values may be rounded for readability. Keep appropriate precision for intermediate calculations and check the unit labels before using the result.
Frequently asked questions
What does the Standard Error Calculator result mean?
Standard error describes uncertainty in the estimated mean rather than the spread of individual observations.
What should I check before using the standard error calculator?
Use the matching sample standard deviation and describe the sampling design when reporting the result.
Related calculators
- Sample Size Calculator — Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.
- Standard Deviation Calculator — Calculate population or sample standard deviation, variance, mean, sum, and count.
- Percent Error Calculator — Calculate percentage error and absolute error between observed and reference values.
- Margin of Error Calculator — Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.
- Mean Absolute Deviation Calculator — Measure the average absolute distance of data values from their arithmetic mean.
- Average Calculator — Calculate the mean, median, mode, and range of any set of numbers.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample 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.