Standard Deviation Calculator
Population and sample standard deviation from a list of numbers.
Guide: Standard Deviation Calculator
Measure spread around the mean with standard deviation. Enter numbers separated by commas or spaces, choose sample or population mode, and read the mean and standard deviation. Variance is the square of standard deviation; reporting both is common in science, while business dashboards often show only σ or s for readability.
Sample vs population
Use population standard deviation when your list is the entire population. Use sample (divide by n−1) when data are a sample estimating a larger population.
The n−1 Bessel correction removes bias so sample variance is unbiased for the population variance under random sampling assumptions.
Interpreting magnitude
Standard deviation shares units with your data. Compare it to the mean via coefficient of variation when scales differ (e.g., dollars vs counts).
Outliers and robustness
One extreme value inflates standard deviation heavily. Median absolute deviation or IQR rules are alternate spread metrics when tails are messy.