Standard Error Calculator
Find the standard error of the mean of a sample, with the sample standard deviation and steps.
Change the values and press Calculate to work out your own figures.
Enter a sample of numbers.
Show the working
- s = √(Σ(x − mean)² ÷ (n − 1)) = 12.3027290817
- SE = s ÷ √n = 12.3027290817 ÷ √8 = 4.34967158038
How to use it
Enter a sample of numbers.
Paste or type the numbers separated by commas, spaces or new lines. Results are worked out exactly and shown to 12 significant figures; Show the working lists each step.
Key facts
SE = s ÷ √n
What the standard error measures
It estimates how much the sample mean would vary from sample to sample. It shrinks as the sample grows: four times the data halves the standard error.
Questions
How do I calculate the standard error?
Divide the sample standard deviation by the square root of the sample size.
Standard error or standard deviation?
SD describes the data; SE describes how precisely the mean is estimated.
Formulas
SE = s ÷ √n
Sources
Limitations
- Up to 5,000 values. Values are separated by commas, spaces or new lines, so write 1250 rather than 1,250.