Standard Error Calculator

How it is calculated

The standard error of the mean is SEM = SD ÷ √n, where SD is the standard deviation of your sample (in the same unit as the data) and n is the number of observations. The result is in the same unit as SD and is shown to four decimal places. The tool returns nothing if SD is negative or if n is below 1. It does not check that n is a whole number, so enter the real count of observations. It only divides: it does not compute SD from raw data, and it does not apply a t or z multiplier, so it gives no confidence interval by itself.

Common mistakes

• Reporting SEM when the goal is to describe how spread out the individual values are. That is the job of the standard deviation.
• Entering the variance instead of the standard deviation. The variance must be square-rooted first.
• Entering n − 1 (degrees of freedom) instead of the sample size n.
• Expecting SEM to halve when the sample doubles. It shrinks by a factor of √2, so you need four times the data to halve it.
• Treating SEM as a 95% interval. A confidence interval needs the SEM multiplied by a t or z value, roughly 2 for large samples.