Standard Error Calculator
Compute the standard error SE = σ/√n from a standard deviation and sample size.
Input Data
Standard deviation of the data.
Number of observations (positive integer).
Results
SE = σ / √n。
1.5
At a glance:Standard error SE = σ/√n quantifies how much a sample statistic varies across repeated samples.
Formula
SE = σ / √n
$$SE = \frac{\sigma}{\sqrt{n}}$$How to Use
- Enter the standard deviation σ (or sample SD s).
- Enter the sample size n (positive integer).
- The calculator outputs the standard error SE = σ / √n.
- SE is commonly used to build confidence intervals: x̄ ± z·SE.
FAQ
How is standard error different from standard deviation?
Standard deviation describes the spread of individual observations; standard error describes how much a sample statistic (e.g. the mean) varies across repeated samples. Larger samples give a smaller standard error.
How does sample size affect the standard error?
Standard error is inversely proportional to the square root of the sample size (SE ∝ 1/√n). Quadrupling the sample size halves the SE.
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.