Standard Deviation Calculator
Calculate population or sample standard deviation from a list of numbers. Also shows mean and count. Paste comma-separated values.
How to calculate Standard Deviation
Standard deviation measures how spread out numbers are around their mean. A low standard deviation means data points cluster close to the average; a high one means they are widely scattered. It is the most widely used measure of statistical dispersion.
Population standard deviation (σ) is used when your data represents the entire group you're studying. The formula is σ = √(Σ(xᵢ − μ)² / N). Sample standard deviation (s) is used when your data is a sample drawn from a larger population: s = √(Σ(xᵢ − x̄)² / (N−1)). The N−1 denominator (Bessel's correction) compensates for the bias in estimating a population parameter from a sample.
For example, test scores of 70, 75, 80, 85, 90 have a mean of 80 and a population standard deviation of approximately 7.07.
Standard deviation is used everywhere: quality control in manufacturing, financial risk assessment (volatility), psychology research, weather forecasting, and medical clinical trials. In a normal distribution, 68% of data falls within one standard deviation of the mean, and 95% within two. Enter your numbers separated by commas to get the result instantly.