The formula this calculator uses
Variance and standard deviation
Mean (μ) = Sum ÷ Count
Population Variance = Sum of (x − μ)² ÷ N
Sample Variance = Sum of (x − μ)² ÷ (N − 1)
Standard Deviation = √Variance
A small standard deviation means values cluster tightly around the mean; a large one means they're spread out.
Population vs. sample standard deviation
This calculator shows both versions. Population standard deviation is used when your numbers represent an entire group you care about. Sample standard deviation, which divides by one less than the count, is used when your numbers are a sample drawn from a larger population — the smaller divisor corrects for the fact that a sample tends to slightly underestimate the true spread of the full population.
How to use this calculator
- Type your numbers separated by commas or spaces.
- The mean, variance, and both standard deviations update instantly.
Frequently asked questions
What does standard deviation measure?
How spread out a set of numbers is around its average — a low value means the numbers are close together, a high value means they're spread out.
What's the difference between population and sample standard deviation?
Population standard deviation divides by the total count (N); sample standard deviation divides by N minus 1, which corrects for typically underestimating spread when working from a sample rather than a whole population.
Which one should I use?
Use population standard deviation if your data is the entire group of interest. Use sample standard deviation if your data is a subset drawn from a larger population.
Why is variance squared before averaging?
Squaring makes every deviation positive (so they don't cancel out) and gives larger deviations proportionally more weight; taking the square root at the end brings the result back to the original unit.