Instant population & sample standard deviation, variance, and mean
Enter Your Numbers
Results
Population Std Dev (σ)
3.815757
Treats data as the full population
Sample Std Dev (s)
4.022161
Applies Bessel's correction (÷ n−1)
Population Variance (σ²)
14.56
Average squared deviation
Sample Variance (s²)
16.177778
Unbiased estimate of population variance
How It Works
Population Std Dev (σ)
σ = √( Σ(xᵢ − μ)² / N )
Use when your data IS the entire population.
Sample Std Dev (s)
s = √( Σ(xᵢ − x̄)² / (N−1) )
Use when your data is a sample from a larger population (Bessel's correction).
The standard deviation calculator instantly computes both population standard deviation (σ) and sample standard deviation (s) from any set of numbers. Paste or type values separated by commas, spaces, or new lines and get variance, mean, sum, min, max, and range in one click — no sign-up required. Perfect for statistics homework, data analysis, quality control, and research.
Population standard deviation (σ) divides by N and is used when your data represents the entire group. Sample standard deviation (s) divides by N−1 (Bessel's correction) and is used when your data is a subset drawn from a larger population, giving an unbiased estimate of the true variability.
Type or paste your numbers into the input box. You can separate them with commas, spaces, tabs, or new lines — any combination works. The calculator automatically ignores blank entries and non-numeric tokens and tells you if any values were skipped.
Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance, which brings the result back to the same unit as your original data. A higher value means more spread; a value near zero means the numbers are clustered closely around the mean.
Use standard deviation when you need a spread measure in the same units as your data (e.g., centimetres, dollars). Variance is preferred in statistical formulas and when combining independent variables, because variances add together while standard deviations do not.