Calculators
Standard Error Calculator
Calculate the standard error of the mean from a dataset or from standard deviation and sample size locally in your browser.
Enter a dataset to compute the standard error of the mean directly, or switch to standard deviation and sample size mode if you already have those values. The calculation runs locally in your browser; your values are not uploaded or stored.
Find the standard error of the mean without uploading your data.
Enter a dataset to compute the sample standard deviation and standard error of the mean directly, or switch to standard deviation and sample size mode if you already have those values. The standard error of the mean (SEM) is the sample standard deviation divided by the square root of the sample size: SEM = s / √N. A smaller standard error indicates the sample mean is a more precise estimate of the population mean. The sample standard deviation uses N − 1 in the denominator. Everything runs locally in your browser, so your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the standard error of the mean (SEM)?
The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample mean. It estimates how far the sample mean is likely to be from the true population mean. It is calculated as SEM = s / √N, where s is the sample standard deviation and N is the sample size.
How does the calculator compute the standard error?
In dataset mode, it calculates the sample standard deviation (dividing by N − 1) from your values, then divides by the square root of the sample size. In standard deviation and sample size mode, it uses the standard deviation and sample size you provide directly with SEM = s / √N.
When should I use dataset mode versus standard deviation and sample size mode?
Use dataset mode when you have the raw data values and want the calculator to compute everything. Use standard deviation and sample size mode when you already know the sample standard deviation and sample size, for example from a published study or previous analysis.
How should I interpret the standard error result?
A smaller standard error means the sample mean is a more precise estimate of the population mean. Standard error decreases as sample size increases, and it is used to construct confidence intervals and perform hypothesis tests about the mean.
Do my values stay private?
Yes. The calculation and copy action run locally in your browser. CodeASystem does not upload or store the values you enter.