Standard Error Calculator
Calculate the standard error of the mean from a data set or from standard deviation and sample size.
Enter your data set. Invalid values will be ignored.
Standard Error of the Mean (SE)
Mean (x̄)
Sample Standard Deviation (s)
Count (n)
Steps
What the Standard Error Measures
The standard error of the mean (SEM) measures how precisely the sample mean estimates the true population mean. It tells you how much sample means would vary if you repeatedly drew samples of the same size from a population. A smaller standard error indicates a more reliable estimate of the mean.
How It Is Calculated
The standard error is the sample standard deviation divided by the square root of the sample size. This calculator uses the sample standard deviation (with Bessel's correction, dividing by n − 1).
- Mean: x̄ = Σxᵢ / n
- Sample SD: s = √( Σ(xᵢ − x̄)² / (n − 1) )
- Standard Error: SE = s / √n
Why Sample Size Matters
Because the standard error divides by the square root of n, larger samples produce smaller standard errors. This is why increasing sample size improves the precision of the estimated mean. At least two values are required to compute the sample standard deviation.