Standard Deviation Calculator
Calculate the standard deviation, variance and basic statistics for any dataset — population (σ) or sample (s) version.
How to use the Standard Deviation Calculator
- Enter your inputs into the Standard Deviation Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The standard deviation formulas
σ (population) = √(Σ(x − μ)² / N) · · · s (sample) = √(Σ(x − x̄)² / (n − 1))
Standard deviation measures spread around the mean. Population uses N in the denominator; sample uses n − 1 (Bessel's correction) to give an unbiased estimate of the true population SD from a sample.
Worked example
Dataset: 4, 8, 6, 5, 3. Mean = 5.2. Deviations squared: 1.44, 7.84, 0.64, 0.04, 4.84. Sum = 14.8. Population SD = √(14.8/5) ≈ 1.72. Sample SD = √(14.8/4) ≈ 1.92.
Frequently asked questions
Should I use population or sample SD?
Sample SD (n − 1) when your data is a subset used to estimate a larger population. Population SD (N) when you have the entire population's data.
What does standard deviation measure?
How spread out values are around the mean. About 68% of values fall within ±1 SD of the mean in a normal distribution; 95% within ±2 SD; 99.7% within ±3 SD.
What about non-normal data?
SD is still a valid spread measure but the 68/95/99.7 rule doesn't apply. For skewed or heavy-tailed data, consider interquartile range (IQR) as an alternative.