How to use the Standard Deviation Calculator
- Paste or type your data values.
- Choose sample (most common) or population.
- Read the standard deviation, variance and summary statistics, and check the step table.
How to calculate standard deviation
- Find the mean: add the values and divide by how many there are.
- Subtract the mean from each value and square the result.
- Add the squares together (the sum of squares).
- Divide by n − 1 for a sample, or by N for a whole population. This is the variance.
- Take the square root of the variance.
Sample or population?
Use population standard deviation (σ) only when your data includes every member of the group you care about — every student in one class, for example. If the data is a sample used to estimate a larger group, use sample standard deviation (s). Dividing by n − 1 (Bessel’s correction) corrects the tendency of a sample to underestimate spread.
What does standard deviation tell you?
It measures how spread out values are around the mean, in the same units as the data. In a roughly normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three (the empirical rule).
Compare spread across two datasets
Enter Dataset B to compare count, mean and standard deviation with Dataset A under the same sample/population setting. A zero baseline spread is handled without a misleading percentage.