Standard Deviation Calculator
Calculate the standard deviation of a dataset.
Runs locally in your browser
Your inputs are processed locally in your browser and are not uploaded or stored by us.
Calculate the standard deviation of a dataset. Standard deviation measures how spread out values are around their mean.
How to calculate standard deviation
- Enter numeric values into the dataset list.
- Select whether your data represents an entire "Population" or a "Sample".
- Click "Calculate" to compute the standard deviation and variance.
Standard Deviation Formulas
Population σ = √[Σ(xᵢ − μ)² / N]
Sample s = √[Σ(xᵢ − x̄)² / (N − 1)]
Population standard deviation is used when the entered values are the full population being described. Sample standard deviation is used when the entered values are a sample used to estimate variability in a larger population. Internally, the calculator uses a numerically stable variance algorithm instead of a fragile difference-of-large-squares formula, reducing floating-point error for large, closely spaced values.
Calculating population standard deviation
Dataset2, 4, 4, 4, 5, 5, 7, 9
TypePopulation
Mean = 5
Population variance = 4
Standard deviation = √4
Result: 2
Notes
- Population standard deviation requires a minimum of 1 value. Sample standard deviation requires a minimum of 2 values.
- For a single population value, the standard deviation is 0.
- A tiny negative result caused only by floating-point noise near zero may be normalized to zero. Materially invalid negative variance is not silently treated as valid.
- These statistics use JavaScript floating-point numbers, so some decimal results may be approximate.
- Your calculator inputs are processed locally in your browser and are not uploaded or stored by us.