Calculators & Converters
Standard Deviation Calculator
The Standard Deviation Calculator takes a list of numbers and calculates both the variance and standard deviation, for either an entire population or a sample drawn from a larger group, showing how spread out the values are from the mean. It's aimed at students working through statistics coursework, researchers doing a quick sanity check on a data set, or anyone who needs to measure variability in a set of numbers.
The calculation happens instantly in your browser the moment you enter your data, using standard statistical formulas, with no server involved and no data leaving your device. That makes it easy to paste in a data set, review the spread, then adjust values and immediately see how the standard deviation changes.
How to Use the Standard Deviation Calculator
- Open the Standard Deviation Calculator tool.
- Paste or type your list of numbers, separated by commas, spaces or new lines.
- Choose whether your data represents the full population or a sample.
- View the calculated variance and standard deviation, updated instantly as you edit the data.
Frequently Asked Questions
What's the difference between population and sample standard deviation?
Population standard deviation divides by the total count of values (n), while sample standard deviation divides by one less (n - 1) to correct for the bias of estimating from a subset, which typically gives a slightly larger result.
What formula does the calculator use?
It calculates the mean, finds the squared difference of each value from the mean, averages those squared differences (using n or n - 1 depending on the mode chosen) for the variance, then takes the square root to get the standard deviation.
How many numbers do I need to enter for a meaningful result?
You need at least two values to calculate a standard deviation at all, and in general, larger data sets tend to give a more stable and representative measure of spread.