Standard Deviation Calculator
Calculate the standard deviation, variance and mean of a data set.
Assumptions used in this calculation
- Both variants shown: Both population (÷n) and sample (÷n−1) standard deviation and variance are calculated; choosing the right one depends on whether your data is the full population or a sample.
About this calculator
Standard deviation tells you how spread out a data set is around its mean, but calculating it by hand means finding the mean first, then squaring every deviation from it, summing those squares, dividing by n or n−1 depending on whether your data is a full population or a sample, and finally taking a square root, a lot of steps to get wrong in a row. This calculator runs that whole process for both interpretations at once: population standard deviation (σ = √(Σ(x − mean)² ÷ n)), used when your data set is the entire population you care about, and sample standard deviation (dividing by n−1, Bessel's correction), used when your data is a sample meant to estimate a larger population's spread, which is the more common case in surveys and experiments. It reports both variance and standard deviation for each, since variance is the intermediate squared value before the final square root. That removes the multi-step manual arithmetic and the ambiguity of picking the wrong denominator for your situation.
Worked example
2, 4, 4, 4, 5, 5, 7, 9
Result: Population std dev = 2, sample std dev ≈ 2.14
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