Standard Error of the Mean Calculator

How to use this calculator

Paste your sample data. The standard error, standard deviation, sample size and mean are calculated.

Formula

SE = s ÷ √n

Worked example

Data: 12, 15, 11, 14, 13, 16, 12, 14, 15, 13

• Mean = 13.5, s = 1.581
• SE = 1.581 ÷ √10 = 0.500
• Approximate 95% interval: 13.5 ± 1.00

Sample size effect

To halve the standard error you need four times as many observations.

Frequently asked questions

What is the standard error?

The standard deviation of the sample mean — how much the mean would vary if you repeated the sampling.

How is it different from standard deviation?

SD describes spread in the data; SE describes uncertainty in the mean. SE = SD ÷ √n, so it shrinks as the sample grows.

How is SE used?

To build confidence intervals — roughly, mean ± 2 SE gives a 95% interval.

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