Free standard deviation calculator: enter numbers to get standard deviation, variance, mean and sum for a population or sample, with the exact formula.
The standard deviation tells you how spread out a set of numbers is: small values mean the data clusters tightly around the average, large values mean it is widely scattered. It is one of the most used statistics in homework, quality control and finance.
This standard deviation calculator works with up to five numbers and gives the standard deviation, variance, mean and sum in one go. Switch between population and sample mode to match your data.
Use population mode when your five numbers are the complete set (for example, all students in a small class). Use sample mode when they are just a sample of a larger group — the calculator then applies Bessel's correction (n − 1) so the estimate is not biased low.
Enter your numbers and choose the mode; the results update instantly. Try the default 10, 12, 23, 23, 16 to see a mean of 16.8 and a population standard deviation of 5.42.
Population divides by n and describes the complete dataset. Sample divides by n − 1 (Bessel's correction) so the estimate from a subset is not biased low.
Use STDEV.P for a population and STDEV.S for a sample; the calculator applies exactly the same formulas.
Squaring removes negative signs and gives more weight to outliers. The variance is the average squared deviation; the standard deviation is its square root, back in the original units.
In a normal distribution about 68% of values lie within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 — the empirical rule.