Standard Deviation Calculator
Calculate sample and population standard deviation, variance, and coefficient of variation. Standard deviation measures how spread out numbers are from the mean.
Inputs
Sample SD (s, n-1)
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Population SD (σ, n)
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Sample variance (s²)
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Mean
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Coefficient of variation
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Within 1 SD of mean
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About Standard Deviation Calculator
Sample vs population
When data is a SAMPLE from a larger population, divide by (n−1) — this corrects bias and gives unbiased estimator. When data IS the entire population, divide by n. Most real-world cases use sample SD.
68-95-99.7 rule
For normally distributed data: ~68% of values lie within 1 SD of the mean, ~95% within 2 SD, ~99.7% within 3 SD. Useful for quick reasoning even when data isn’t strictly normal.
Coefficient of variation
CV = SD ÷ mean × 100%. Unitless — compares spread between datasets with different scales. CV of 10% (tight) vs 50% (highly variable). Useful when SD alone is hard to interpret out of context.