What the result means
Standard deviation measures how far values typically spread around their mean. The population result divides by N; the sample result divides by n−1 to estimate variability in a larger population.
Math
Standard Deviation Calculator
Calculate population and sample standard deviation for six values.
Your last 50 calculations are stored only in this browser, not in a CalcOcean account. Anyone using this browser profile can see them. Clear history on shared devices. Calculation history
How this calculation works
Calculate population and sample standard deviation for six values. Enter your values, select Calculate, then review the result. You can change any value and calculate again.
Formula used
σ = √(Σ(x − μ)² ÷ N) · s = √(Σ(x − x̄)² ÷ (n − 1))
Good to know
Results are estimates for informational purposes.
Example calculation
For 2, 4, 4, 4, 5, 5: population σ = 1
A practical accuracy check
Identical values give zero. For 2, 4, 4, 4, 5, 5, population σ = 1 and sample s ≈ 1.09545 because the latter divides by n−1.
Assumptions and limits
Standard deviation uses the same unit as the data but is sensitive to outliers. A low value does not prove quality or normality, and datasets with different means may need a relative measure such as coefficient of variation.
Using the result responsibly
Choose population when the entered values are the complete group of interest and sample when they represent observations from a larger group. Report the mean, sample size and chosen definition with the result.
A relevant comparison to try
Choose population only for the complete group. For observations representing a larger group, report the sample result with mean, sample size and notable outliers.
How to use this calculator
- Enter your values, select Calculate, then review the result. You can change any value and calculate again.
- Check units and time periods before comparing two results.
- Change one input at a time to understand its effect.
Frequently asked questions
What does the Standard Deviation Calculator calculate?
Calculate population and sample standard deviation for six values. The result is calculated from the values you enter and the formula shown on this page.
Which assumptions does the Standard Deviation Calculator use?
It applies σ = √(Σ(x − μ)² ÷ N) · s = √(Σ(x − x̄)² ÷ (n − 1)). Values, fees, rules or timing not represented by an input are not added automatically.