Standard Deviation Calculator – Variance and Mean
Compute standard deviation, variance, mean, min and max for any set of numbers. Choose population or sample formula. Enter values separated by commas or spaces—ideal for statistics homework, data analysis, quality control and research. Quick, accurate, runs in your browser.
Standard Deviation Calculator
Compute standard deviation, variance and mean for a set of numbers. Choose population (entire set) or sample (subset). Enter values separated by commas or spaces.
How the standard deviation formula works
Standard deviation is the square root of variance:
Population: σ = √[ Σ(x − μ)² / N ]
Sample: s = √[ Σ(x − x̄)² / (n − 1) ]
- μ or x̄ = mean
- N or n = count
- Σ = sum of squared deviations from mean
Sample formula uses n−1 (Bessel's correction) for an unbiased estimate when data is a subset of a larger population.
Standard deviation in statistics and data analysis
Standard deviation is one of the most used measures of spread in statistics. It tells you how much values deviate from the average. In a normal distribution, about 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. It is used in finance (volatility), quality control, research and education.
Use this calculator for homework, data analysis or quick statistical summaries. For more math tools, try the percentage, ratio or discount calculators. All computations run locally with no data stored.