Find the standard error of the mean from raw data or from a mean, standard deviation and sample size, with a 95% interval.
Standard error
How to use this tool
Raw data takes priority when both are present.
They are shown so you can spot a typing error.
The headline figure is the precision of the mean.
It is the range of plausible population means at roughly 95% confidence.
Formula & worked example
Data 2, 4, 4, 4, 5, 5, 7, 9 has mean 5, sample SD 2.138 and standard error 0.756.
Limitations — read this before you rely on it
The 95% interval is a normal approximation; for small samples use a t interval. Results assume the sample is random and the values are independent.
Frequently asked questions
It measures how far a sample mean typically sits from the true population mean: SD divided by the square root of n.
Standard deviation describes the spread of the data; standard error describes the precision of the mean. Bigger samples give smaller standard errors.
It uses 1.96 × SE, which is exact for large samples. Small samples should use a t critical value instead, giving a slightly wider interval.
Yes: comma- or space-separated numbers. The sample standard deviation (n − 1) is used, as usual for samples.
A more precise estimate of the population mean — usually because the sample is larger or less spread out.