Standard Deviation Calculator - Calculate Sample & Population SD

Standard Deviation Calculator

Calculate Standard Deviation with Step-by-Step Analysis & Visualization

Data Input
Separate numbers with commas, spaces, or new lines
Analysis Results

Calculating statistics...

Sample Size (n)
0
Mean (μ)
0.0000
Sum (Σx)
0.00
Range
0.00
Sample SD (s)
0.0000
Population SD (σ)
0.0000
Variance (s²)
0.0000
Coefficient of Variation
0.00%
Data Distribution
Calculation Steps

Enter data and click "Calculate SD" to see step-by-step calculations...

Calculation History
No calculations yet. Start by entering data above.

What is Standard Deviation?

Standard Deviation (SD) is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

How to use this Standard Deviation Calculator?

  • Enter Data: Input your data points separated by commas, spaces, or new lines in the input box above.
  • Calculate: Click the "Calculate SD" button to instantly get results.
  • Analyze: View the Mean, Variance, Population SD, and Sample SD along with a visual graph.
  • Export: Save your results as PDF, CSV, or JSON for your reports.

Population vs Sample Standard Deviation

This tool calculates both types of standard deviation:

  • Population Standard Deviation (σ): Used when your data represents the entire population.
  • Sample Standard Deviation (s): Used when your data is a sample of a larger population. This calculation uses Bessel's correction (n-1).