Calculate standard deviation, variance, and other dispersion statistics for sample or population data
Use when data is a subset of a larger group (divides by n-1)
Enter numbers separated by commas, spaces, or newlines
You might also find these calculators useful
Standard deviation measures how spread out your data is from the mean. Our calculator computes both sample and population standard deviation, along with variance and coefficient of variation. Essential for statistics students, researchers, and data analysts.
Standard deviation (σ for population, s for sample) measures the average distance of data points from the mean. A low standard deviation means data points cluster close to the mean, while a high standard deviation indicates data is spread out. Variance is simply the standard deviation squared.
Standard Deviation Formula
s = √[Σ(xᵢ - x̄)² / (n-1)]Monitor manufacturing consistency and detect variations.
Measure investment risk and portfolio volatility.
Analyze experimental data and report variability.
Understand test score distributions and grading curves.
Use population SD when you have data for the entire group you're studying (like test scores for an entire class). Use sample SD when you're estimating based on a subset (like surveying 100 people from a city). When in doubt, use sample SD—it's more conservative.