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Standard Deviation Calculator

Calculate mean, variance, population & sample standard deviation, and sum of squares.

Numeric Dataset (comma, space, or newline separated)

Result Summary

Sample Std Dev (s)

5.237229

Sample Variance (s²)

27.428571

Mean (Average)

Median

18.5

Count (n)

Sum

144

Population Std Dev (σ)

4.898979

Range (Max - Min)

Standard Error (SEM)

1.85164

How to Use This Calculator

Analyze numeric datasets instantly to compute count, sum, mean, median, range, variance, population (σ) and sample (s) standard deviation, plus z-score variance steps.

1Paste or type numbers separated by commas, spaces, or newlines.
2Choose Sample (N - 1, default for data samples) or Population (N, when every data point is present).
3Inspect mean, median, variance, standard deviation, standard error, and CSV summary.

Standard Formula & Methodology

Sample s = √[ Σ(xi - x̄)² / (n - 1) ] | Population σ = √[ Σ(xi - μ)² / N ]

Helpful Context & Precision Notes

Displays both Sample and Population results simultaneously so you never pick the wrong denominator by accident.

All inputs stay locally inside your browser tab — nothing is uploaded or logged.

Frequently Asked Questions

Use Sample (n-1, Bessel’s correction) when your dataset is a subset drawn from a larger group. Use Population (N) only when you have measurements for the entire population.