Calculate standard deviation, variance, mean, and more for any data set.
Enter a list of numbers, and this calculator returns the mean, variance, and standard deviation for both a full population and a sample — the two most common ways this statistic is calculated, since they use slightly different formulas.
1. Calculate the mean of all the values.
2. Subtract the mean from each value and square the result (this removes negative signs and emphasizes larger deviations).
3. Average those squared differences to get the variance — dividing by the total count (n) for a population, or by n−1 for a sample (Bessel's correction, which adjusts for the fact that a sample tends to underestimate true population variance).
4. Take the square root of the variance to get the standard deviation, back in the original units of the data.
Population standard deviation divides by n (the total count) and is used when you have data for an entire group. Sample standard deviation divides by n−1 and is used when your data is a subset meant to estimate a larger population — dividing by a smaller number slightly inflates the result to correct for sampling bias.
A low standard deviation means the data points are clustered closely around the mean, indicating consistency. A high standard deviation means the data is more spread out and variable.
If you averaged the raw differences from the mean, positive and negative deviations would cancel out, always giving zero. Squaring removes the negative signs so deviations in either direction contribute to the total spread.