✓ Effortless Math · Free Tool

Standard Deviation Calculator

Enter a data set and instantly get the population (σ) and sample (s) standard deviation, variance, mean, and count — with a dot-plot graph and full step-by-step working.

Population:  σ = √( Σ(x − μ)² / N )  ·  Sample:  s = √( Σ(x − x̄)² / (n−1) )
Data set

Separate values with commas or spaces. Decimals and negatives are fine. You need at least two numbers for a sample standard deviation.

Results

Population standard deviation (σ)
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Population std. dev. (σ)
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Sample std. dev. (s)
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Variance (population, σ²)
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Mean (μ = x̄)
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Count (n)
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Graph — dot plot

Data pointsMean

Step-by-step (standard deviation)