Standard Error Calculator
Calculate the standard error of a mean or proportion and its confidence interval.
About the Standard Error Calculator
Choose a mean or a proportion and enter the standard deviation (or proportion) and sample size, or paste raw data. The calculator gives the standard error and a confidence interval.
The standard error measures how much a sample statistic would vary from sample to sample. It shrinks with the square root of the sample size, so quadrupling n halves it. Confidence intervals for a mean use the t distribution (df = n − 1); for a proportion, the normal (Wald) approximation, which is reasonable when np and n(1 − p) are both at least 10.
The formula
SE(mean) = s ÷ √n; SE(proportion) = √(p(1 − p) ÷ n)
Worked example
A sample of 50 with mean 100 and standard deviation 12
- SE = 12 ÷ √50 = 1.697
- 95% confidence interval with t = 2.0096
- 96.59 to 103.41
Questions people ask
Standard error vs standard deviation?
SD describes spread in the data; SE describes precision of the mean.
How do I halve the SE?
Use four times as many observations.