Standard Error Calculator

This calculator finds the standard error of the mean, or SEM, from a set of data, along with the mean, the sample standard deviation and the sample size it is based on. The standard error is one of the most important and most misunderstood quantities in statistics. It measures how precisely your sample mean estimates the true population mean: a small standard error means your sample mean is likely close to the real value, while a large one means it could be well off. Crucially, it is different from the standard deviation. The standard deviation describes how spread out the individual data points are, whereas the standard error describes the uncertainty in the average of those points, and it gets smaller as your sample size grows, because larger samples pin down the mean more tightly. The standard error is the foundation of confidence intervals and hypothesis tests, and it is what error bars on many graphs represent. You paste or type your data, and the calculator returns the standard error, the mean, the sample standard deviation, and the number of data points. The results update as you edit the data, so you can see how adding more observations shrinks the standard error. Use it for research, lab reports, statistics assignments, or any time you report a mean and need to express how reliable it is. Reporting a mean with its standard error, often as mean plus or minus SEM, is standard practice in science. The calculation uses the sample standard deviation divided by the square root of the sample size, exact for your inputs and rounded for display.

Standard error = sample standard deviation / square root of n. It measures the precision of the mean, not the spread of the data. Rounded for display.