Standard Deviation Calculator
Calculate standard deviation, variance, mean and count for a set of numbers, for both samples and populations.
Sample standard deviation
5.64
from 7 values
Sample SD (s)5.64
Population SD (σ)5.2216
Sample variance (s²)31.8095
Population variance (σ²)27.2653
Mean19.8571
Count7
Sum139
Sum of squared deviations190.8571
Use the sample figure unless your numbers represent an entire population.
About the Standard Deviation Calculator
Standard deviation measures how spread out a set of numbers is around its mean. A small value means the data clusters tightly; a large one means it is widely dispersed. Paste or type your numbers separated by commas or spaces.
Formula
Population: σ = √(Σ(x − μ)² / N). Sample: s = √(Σ(x − x̄)² / (N − 1)). The sample version divides by N − 1 (Bessel's correction) to avoid underestimating the spread of the wider population.
Frequently Asked Questions
Use the population formula only when your numbers are the entire group you care about. If they are a sample drawn from a larger population — which is the usual case — use the sample formula, which divides by N − 1.
Variance is the average squared distance from the mean; standard deviation is its square root. Taking the root returns the figure to the original units, which makes it far easier to interpret.
A sample's own mean sits closer to its data than the true population mean does, so squared deviations come out slightly too small. Dividing by N − 1 rather than N corrects that bias.
For roughly bell-shaped data, about 68% of values fall within one standard deviation of the mean and about 95% within two. That makes it a quick way to judge whether a particular value is unusual.
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