Standard Error Calculator

Standard error of the mean from raw data or from SD and n, with a confidence interval.

SEM = s ÷ √n. With a sample standard deviation of 12 and n = 36, SEM = 12 ÷ 6 = 2. The 95% confidence interval for the mean is about x̄ ± 2 × SEM (using t for small samples).

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How to use it

Paste your data, or enter the standard deviation and sample size.
Choose the confidence level.
Read the SEM and the confidence interval for the mean.

What you enter

Data, or standard deviation and sample size
Confidence level

What you get

Standard error of the mean
Mean and SD
Margin of error
Confidence interval

Formula

SEM = s ÷ √n | CI = x̄ ± t(α/2, n−1) × SEM

Worked example

Input: s = 12, n = 36

Result: SEM = 2.0

The sample mean is likely within about ±4 of the population mean (95%).

Questions

How do you calculate standard error?

Divide the sample standard deviation by the square root of the sample size.

What is the difference between SD and SEM?

SD describes how spread out individual values are. SEM describes how precisely the sample mean estimates the population mean, and shrinks as n grows.

Should I report SD or SEM in error bars?

Use SD to show variability in the data and SEM (or a confidence interval) to show precision of the mean. Always say which one you plotted.

How do I get SD from SEM?

Multiply the SEM by √n.

Limitations

Assumes independent observations; the t interval assumes roughly normal data or a large sample.

References

Altman DG, Bland JM (2005) BMJ 331:903.

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.