Standard Deviation Calculator
Work out the sample or population standard deviation of up to 8 numbers to see how spread out your data is around the mean.
Only the first this-many values below are included, so you can use fewer than 8 data points.
Your results
Sample standard deviation divides by n − 1.
Calculation breakdown
- Mean
- x̄ = Σx / n
- Sample variance
- s² = Σ(x − x̄)² / (n − 1)
- Population variance
- σ² = Σ(x − x̄)² / n
- Standard deviation
- SD = √variance
Worked example
A class of 6 students scored 82, 75, 91, 68, 88 and 79 in a test. Treating this as a sample of a larger cohort gives a mean of 80.5 and a sample standard deviation of about 8.4 marks.
Assumptions
- Use 'Sample' when your values are a subset of a bigger group, and 'Population' when they are every member of the group.
- Only the values up to the 'how many values to use' count are included in the calculation.
- This is a general maths tool, not a substitute for statistical software on large or sensitive datasets.
How this calculator works
Enter up to 8 numeric values and choose whether they represent a sample or a full population. The calculator finds the mean, then the sample or population standard deviation, a common measure of how spread out a dataset is around its average.
Frequently asked questions
What's the difference between sample and population standard deviation?
Sample standard deviation divides by n − 1 to correct for using a subset of a larger group, while population standard deviation divides by n when every member is included.
Why does my standard deviation change if I include more values?
Adding more values changes both the mean and the spread around it, so the standard deviation will shift as the dataset changes.
Can I use fewer than 8 values?
Yes, set 'how many values to use' to any number from 2 to 8 and only that many of the fields below will be included.