Standard Error Calculator
The standard error measures the variability of a sample statistic (like the mean) and indicates how close your sample estimate is likely to be to the true population value. This calculator computes the standard error of the mean and the standard error of a proportion. Enter your sample standard deviation and sample size for means, or sample size and estimated proportion for proportions. Smaller standard errors indicate more precise estimates and more reliable conclusions.
Standard error formulas
SE of Mean = SD / sqrt(n)
SE of Proportion = sqrt(p * (1-p) / n)
Margin of Error = z * SE
Interpreting standard error
- Smaller SE = more precise estimate: Your sample mean is closer to the true population mean.
- Larger sample = smaller SE: More data always gives more precision (SE decreases with sqrt(n)).
- 95% confidence interval: mean ± 1.96 * SE (for normally distributed data).
- Rule of thumb: About 95% of samples will have means within 2 * SE of the true population mean.
Standard error: frequently asked questions
What is the standard error?
The standard error (SE) is the standard deviation of the sampling distribution of an estimate (usually the mean). It measures how much sample means vary from the true population mean due to random sampling.
How does standard error relate to standard deviation?
Standard deviation measures variability within a single sample. Standard error measures variability of sample statistics (like the mean) across many samples. SE = SD / sqrt(n), where n is the sample size.
What does a smaller standard error indicate?
A smaller standard error indicates that your sample estimate is more reliable and closer to the true population value. Larger samples always produce smaller standard errors.
Is standard error the same as margin of error?
No. Standard error is the standard deviation of the sampling distribution. Margin of error = z * SE, where z is a critical value based on your desired confidence level.
When should I use standard error?
Use SE to assess the precision of your estimate. Use it when calculating confidence intervals, hypothesis tests, and whenever you need to know how close your sample statistic is likely to be to the population parameter.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
- American Statistical Association: ASA.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.