MihsabaHow to use
Standard error describes the sampling variability of an estimator. This calculator handles the standard error of a mean from s and n, and of a proportion from p and n.
- Choose mean or proportion mode.
- For a mean, enter sample standard deviation s and sample size n.
- For a proportion, enter p as a percentage and sample size n.
- Review SE and the clearly labeled approximate 95% normal margin 1.96×SE.
How it is calculated
Example
Example: with s=12 and n=36, SEM=12/√36=2. With p=40% and n=100, proportion SE≈4.90 percentage points.
Important notes
The displayed 95% margin is a simple normal approximation, not a substitute for a confidence-interval method suited to the problem. Proportion normal approximations can be poor with small expected counts.
Frequently asked questions
Standard deviation versus standard error?
Standard deviation describes spread in observations; standard error describes sampling variation of an estimator such as the mean.
Why does SE shrink as n grows?
For a mean, SE is proportional to 1/√n, so larger samples reduce sampling uncertainty.
Does 1.96×SE always give a valid confidence interval?
No. It is a normal approximation and some settings require a different method.
Is this calculator free?
Yes. It is free to use and requires no account.