Standard Error Calculator
Calculate the standard error of the mean (SEM) from the standard deviation and sample size.
How to use this tool
- Enter standard deviation (s) and sample size (n) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your standard error (se) and the full breakdown beneath it.
Standard Error = s / √n. Quantifies how much the sample mean is expected to differ from the true population mean.
Formula
Standard Error (SE) = s ÷ √n
Where s is the sample standard deviation and n is the sample size.
How it works
This calculator computes the standard error of the mean by dividing the sample standard deviation by the square root of the sample size. The standard error quantifies how much the sample mean is expected to vary from the true population mean. It assumes the input standard deviation is already calculated from the sample and that observations are independent.
Worked example
Worked example
- Standard deviation s = 10, sample size n = 25
- Calculate √n = √25 = 5
- SE = s ÷ √n = 10 ÷ 5 = 2
Standard error (SE) = 2.0
Key terms
- Standard error of the mean (SEM)
- An estimate of how much the sample mean would vary if the study were repeated many times; equals s ÷ √n.
- Standard deviation (s)
- A measure of how spread out individual observations are around the sample mean.
- Sample size (n)
- The number of observations in the sample; larger samples yield a smaller standard error.
- Sampling distribution
- The theoretical distribution of sample means calculated from many repeated samples of the same size.
- Precision
- As standard error decreases (larger n or smaller s), the sample mean becomes a more precise estimate of the population mean.
Frequently asked questions
- What is the difference between standard deviation and standard error?
- Standard deviation (SD) describes the variability of individual data points around their mean. Standard error (SE) describes the variability of the sample mean itself — it shrinks as sample size grows: SE = SD / √n.