Home›Maths›Standard Deviation Calculator

📊 Standard Deviation Calculator

Enter your data values (comma or space separated) to calculate population and sample standard deviation, mean, variance and more.

About the Standard Deviation Calculator

The Standard Deviation Calculator accepts any set of numbers and computes a full descriptive statistics summary. It distinguishes between population standard deviation (σ) — used when your data represents the entire population — and sample standard deviation (s) — used when your data is a sample from a larger population (divides by n−1 using Bessel's correction). All calculations run in your browser; no data is stored.

Formulas Used

Mean: μ = Σx / n

Population Variance: σ² = Σ(x − μ)² / n

Sample Variance: s² = Σ(x − μ)² / (n − 1)

Standard Deviation: σ = √σ²  |  s = √s²

What Does Standard Deviation Tell You?

Standard deviation measures the spread or dispersion of a data set. A low standard deviation means most values are close to the mean; a high standard deviation means values are spread over a wider range. It is one of the most fundamental tools in statistics, used in science, finance, quality control, and social research.

Population vs. Sample Standard Deviation

Use population standard deviation (σ) when you have data for the entire group you are studying — for example, the test scores of all students in a specific class. Use sample standard deviation (s) when your data is a subset of a larger population — for example, a random sample of 50 employees from a company of 5,000. Sample SD uses n−1 in the denominator to correct for the underestimation of variance that occurs with small samples.

Other Statistics Computed

  • Mean (average) — the central value of the data set
  • Median — the middle value when sorted; less sensitive to outliers than the mean
  • Range — the difference between the maximum and minimum values
  • Variance — the square of the standard deviation, useful for statistical tests
  • Count (n) — the number of data points entered
⚠️
Important Note: This tool is intended to provide estimates and should not be used as a substitute for professional advice. Information generated by these calculators may be incomplete and does not account for all individual circumstances. Always seek the counsel of a certified expert (such as a financial advisor, healthcare provider, or licensed engineer) before taking action based on these results.

Related Calculators