Standard Deviation Calculator
Sample and population spread, variance and standard error.
Enter your values
ⓘ Live results
Results
- Sample standard deviation
- 2.160247
- Population standard deviation
- 2
- Sample variance
- 4.666667
- Mean
- 6
- Standard error of the mean
- 0.816497
Working
- 1n = 7, Σ(x − x̄)² = 28
Quick answer
Standard deviation measures average distance from the mean; sample SD divides by n−1, population SD by n.
s = √(Σ(x − x̄)² ÷ (n − 1))
How to use the Standard Deviation Calculator
- 1Paste your data separated by commas.
- 2Use sample SD for a sample, population SD for a full population.
- 3Read variance and standard error too.
Worked example
Using the values the calculator loads with:
Inputs
- Data (comma separated)4, 8, 6, 5, 3, 9, 7
Results
- Sample standard deviation2.160247
- Population standard deviation2
- Sample variance4.666667
- Mean6
- Standard error of the mean0.816497
- n = 7, Σ(x − x̄)² = 28
Frequently asked questions
Why divide by n − 1?
Bessel's correction. A sample mean sits closer to its own data than the true mean, so dividing by n underestimates the spread.
What does one SD mean?
In a normal distribution, about 68% of values fall within one standard deviation of the mean.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.