Standard Deviation Calculator
The Standard Deviation Calculator finds the mean, variance, and standard deviation of any data set, letting you choose between sample and population statistics.
Standard Deviation
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How standard deviation is calculated
Standard deviation measures how spread out a set of numbers is from its mean (average). First, the mean is calculated, then the average squared distance from the mean (variance), then the square root of that:
Mean: μ = Σx / n
Variance: σ² = Σ(x − μ)² / n (population)
Variance: s² = Σ(x − μ)² / (n−1) (sample)
Standard Deviation = √Variance
Example: For the data set 10, 12, 23, 23, 16, 23, 21, 16, the mean is 18, and the sample standard deviation is approximately 5.24.
Sample vs. population
Use "population" when your data represents the entire group you care about. Use "sample" (which divides by n−1 instead of n) when your data is a subset used to estimate the characteristics of a larger population — this is the more common case in statistics and research. See our Scientific Calculator for other calculations.