Standard Error of the Mean Calculator
Standard error from sample standard deviation and size.
Enter your values
ⓘ Live results
Results
- Standard error
- 2
- Sample size
- 36
- 95% margin of error (approx)
- ±3.92
Quick answer
The standard error of the mean is the sample standard deviation divided by the square root of the sample size.
SE = s / sqrt(n)
How to use the Standard Error of the Mean Calculator
- 1Enter the sample standard deviation.
- 2Enter the sample size used to compute it.
- 3The standard error shrinks as the sample size grows, following a square-root relationship.
Worked example
Using the values the calculator loads with:
Inputs
- Sample standard deviation12
- Sample size36
Results
- Standard error2
- Sample size36
- 95% margin of error (approx)±3.92
Frequently asked questions
Why divide by sqrt(n) instead of n?
Variance of the mean scales as variance/n, so standard deviation of the mean scales as s/sqrt(n).
How is SE different from standard deviation?
Standard deviation measures spread of individual data points; standard error measures the precision of the sample mean estimate.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.