Standard Deviation Calculator
Standard deviation is the square root of variance. Use the free calculator to get both for a sample or a population, with every step shown.
Open the variance calculatorCalculate standard deviation now
Open the variance calculator, paste your numbers (commas, spaces, or spreadsheet columns all work), and choose sample or population. The result panel shows the standard deviation alongside the variance, mean, count, and sum of squares.
Formulas
Sample standard deviation: s = √( Σ(x − x̄)² / (n − 1) )
Population standard deviation: σ = √( Σ(x − μ)² / N )
Sample or population?
Choose population when your data includes every member of the group (for example, all test scores in one class). Choose sample when your data is a subset used to estimate a larger group. When unsure, sample is the safer choice.
Example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the sum of squares is 32. Population standard deviation is √(32 / 8) = 2; sample standard deviation is √(32 / 7) ≈ 2.1381. The full method is inhow to calculate variance.
Frequently asked questions
How do I calculate standard deviation?
Find the variance (the average squared distance from the mean, dividing by n − 1 for a sample or N for a population), then take its square root.
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides the sum of squares by N and describes a full population. Sample standard deviation (s) divides by n − 1 and estimates the population's spread from a sample.
Is standard deviation the square root of variance?
Yes. s = √s² and σ = √σ². Standard deviation shares the units of your data, while variance is in squared units.
Does the calculator upload my data?
No. Everything runs in your browser; nothing you paste is sent to a server.