Standard Deviation Calculator
Calculate population and sample standard deviation for any dataset.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
Can't find what you need?
Request a ToolHow to Use the Standard Deviation Calculator
Enter your numbers separated by commas or spaces in the input field above. The calculator processes your data instantly and shows both population and sample standard deviation. Population standard deviation divides by n, while sample standard deviation divides by n-1 (Bessel's correction) to give an unbiased estimate when working with a subset of a larger population.
The result card displays the sample standard deviation as the primary result, since most real-world calculations use sample data. Below it you will find population standard deviation, the mean, and the count of values entered. Use the Copy button to grab the result or Share to send a pre-filled link to someone else.
About Standard Deviation
Standard deviation measures how spread out values are from the mean. A low standard deviation means values cluster tightly around the average, while a high standard deviation indicates wide dispersion. It is the square root of variance and is expressed in the same units as the original data, making it easier to interpret than variance. Standard deviation is foundational in statistics, used in quality control, finance (volatility), science, and anywhere you need to quantify variability.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation divides the sum of squared differences by n (the total count). Sample standard deviation divides by n-1, which corrects for bias when estimating from a sample rather than measuring the entire population. Use sample (n-1) when your data is a subset. Use population (n) when you have every member of the group.
How do I interpret a standard deviation value?
Compare the standard deviation to the mean. A standard deviation that is small relative to the mean suggests low variability. A common benchmark is the coefficient of variation (CV = std dev / mean x 100). A CV below 15% is generally considered low variability. For normally distributed data, about 68% of values fall within one standard deviation of the mean, and 95% within two.
Can I calculate standard deviation for grouped data?
This calculator works with raw (ungrouped) data. For grouped data with class intervals, you would use the midpoint of each class multiplied by its frequency. Enter the expanded dataset (repeat each midpoint by its frequency) into this calculator, or use the weighted average calculator paired with variance calculations.