Standard Error Calculator
Estimate how much a sample mean is likely to bounce around, either from your raw numbers or from a standard deviation and sample size you already have.
From a list of values
Already know the standard deviation and sample size?
How it works
The standard error of the mean tells you how precise your sample average is. The formula is SEM = s ÷ √n, where s is the standard deviation and n is how many values you collected.
Paste a list and the calculator does the middle steps for you: it finds the mean, works out the sample standard deviation, then divides by the square root of the count. If you already know s and n, the second box skips straight to the division.
With a standard deviation of 12 and a sample of 36, the standard error is 12 ÷ √36 = 12 ÷ 6 = 2. Quadruple the sample to 144 and it halves to 1 — bigger samples pin the mean down tighter.
Frequently asked questions
What's the difference between standard error and standard deviation?
Standard deviation describes how spread out the individual data points are. Standard error describes how spread out the sample mean would be if you repeated the study many times. One is about the data, the other about the average of the data.
Why does a bigger sample shrink the standard error?
Because you divide by the square root of the sample size. More observations average out random noise, so the mean settles closer to the truth. The catch is the square root — to cut the error in half you need four times the data.
Can I use it to build a confidence interval?
That's exactly what it's for. A rough 95% confidence interval is the mean plus or minus about two standard errors. So a small standard error gives a tight interval and a more confident estimate of where the true mean lies.
Which standard deviation should I plug in?
Use the sample standard deviation — the one with the n − 1 divisor — since the standard error is about estimating a population from a sample. The list mode already computes that for you.