Standard Deviation Calculator 🔒 Your data never leaves your browser.
Calculate mean, variance and standard deviation (population or sample).
About this tool
This standard deviation calculator takes any list of numbers and works out the count, mean, variance and standard deviation — both the population and sample versions — right in your browser. Paste in values separated by commas, spaces or new lines and the results update as you type, using the same formulas taught in statistics courses and spreadsheets alike.
Not sure which version to use? Population standard deviation (dividing by N) is correct when your numbers already represent the entire group you care about — every student in a class, every day of last month. Sample standard deviation (dividing by N−1, known as Bessel's correction) is correct when your numbers are just a sample drawn from a larger population you want to estimate — a survey of 50 customers standing in for all customers. When in doubt, the sample version is the safer default for real-world data.
Frequently asked questions
Which one should I use — population or sample standard deviation?
Use population standard deviation when your data represents the ENTIRE group you care about — e.g. the test scores of every student in one specific class. Use sample standard deviation when your data is a subset meant to estimate a larger, unmeasured population — e.g. surveying 200 customers to estimate satisfaction across your entire customer base. Sample standard deviation divides by (n−1) instead of n, which slightly inflates the result to correct for the fact that a sample tends to underestimate the true population variance (this correction is called Bessel's correction).