Standard Deviation Calculator
Calculate population and sample standard deviation, variance, mean, count, and sum from a list of numbers.
Standard deviation and variance
This calculator computes six statistics from a list of numbers. Population standard deviation (σ) measures how spread out values are relative to the mean, dividing by N. Sample standard deviation (s) uses N−1 in the denominator (Bessel's correction) to give an unbiased estimate when your data is a sample from a larger population. Variance is the squared population standard deviation. All computation runs locally in your browser — nothing is sent to any server.
Enter numbers separated by commas, spaces, or line breaks. You can paste directly from a spreadsheet column or a CSV row. The tool updates as you type.
FAQ
When should I use population vs. sample standard deviation? Use population SD when you have data for the entire group you care about. Use sample SD when your data is a subset and you want to estimate the variability of the full population.
Why does sample SD show 0 for a single number? With only one value, N−1 equals zero and the formula is undefined. The calculator returns 0 rather than an error because a single data point carries no information about spread.
What is Bessel's correction? Dividing by N−1 instead of N corrects the bias that arises when estimating population variance from a sample. With small samples the difference is noticeable; as N grows large, the two values converge.