Standard Deviation Calculator
Calculate population and sample standard deviation, variance, mean, count, sum, and range for any dataset.
Enter values and click Calculate SD to see results
Formula
What is Standard Deviation?
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation means data points are close to the mean, while a high standard deviation indicates data is spread out.
Population vs Sample Standard Deviation
Use population SD (σ) when you have data for the entire population. Use sample SD (s) when working with a sample from a larger population.
Sample Variance: s² = Σ(xᵢ − x̄)² / (N − 1)
Standard Deviation = √Variance
The sample variance divides by (N − 1) instead of N to correct for bias — this is known as Bessel's correction.
Interpreting Standard Deviation
In a normal distribution, approximately 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD. This is known as the 68-95-99.7 rule.
Related Tools
For basic averages, use our Average Calculator. For counting arrangements, try the Permutation & Combination Calculator.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population SD divides by N (when you have all data points). Sample SD divides by N-1 (Bessel's correction) when you have a subset. Use sample SD for most real-world data analysis.
Is this calculator free, and do I need to sign up?
Yes, it is completely free with no sign-up. There are no usage limits and no paywalls.
Are my inputs saved or sent to any server?
No. Every calculation happens entirely in your browser. Nothing you type is uploaded, logged, or shared with us or any third party.