Standard Error Calculator
Enter a sample's standard deviation and sample size to calculate the standard error of the mean — a measure of how much a sample mean is likely to vary from the true population mean.
How the Standard Error formula works
The standard error formula:
Standard error = Standard deviation / √(sample size)
Step-by-step calculation
- Take the square root of the sample size.
- Divide the standard deviation by that square root.
Worked example
A standard deviation of 12 with a sample size of 50: Standard error = 12 / √50 ≈ 12/7.07 ≈ 1.70.
Frequently asked questions
How is standard error different from standard deviation?
Standard deviation measures spread within a single data set. Standard error estimates how much a sample's mean would vary if you repeated the sampling process — it shrinks as sample size grows, reflecting greater confidence in a larger sample's mean.
Why does a larger sample size reduce standard error?
Because it's divided by the square root of sample size — as samples get larger, the sample mean becomes a more stable, reliable estimate of the true population mean, which is reflected in a smaller standard error.