Standard Error Calculator

How it is calculated

The tool gives the standard error of the mean (SEM): SEM = s / √n, where s is the sample standard deviation and n is the number of observations. It shows how precisely the sample mean pins down the true mean, not how spread out individual values are. SEM is in the same unit as the data and is shown with four decimals. Quadrupling the sample size halves the SEM. The standard deviation must be zero or more, and n must be a whole number of at least 2: a single observation (n = 1), a fractional n such as 36.5, or a negative standard deviation gives no result. A standard deviation of 0 is accepted and gives an SEM of 0.0000.

Common mistakes

• Reporting SD and SEM interchangeably. SD describes the spread of the data, SEM the uncertainty of the mean, and SEM is smaller whenever n is above 1.
• Entering the variance instead of the standard deviation. Take the square root of the variance first.
• Entering the number of groups or the degrees of freedom (n − 1) as n. The formula uses the sample size, and n = 1 shows no result because one observation has no standard deviation.
• Expecting precision to improve linearly. To halve the SEM you need four times as many observations.
• Using the population standard deviation without noting it. The tool takes whatever SD you supply and does not tell the two apart.