Standard Deviation Calculator

Compute sample (n−1) and population (n) standard deviation from a list of numbers.

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Result

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General calculation reads

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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Paste your numbers (commas, spaces, or newlines).
  • Read both sample and population SD.

About this calculator

Standard deviation measures spread — how far values typically fall from the mean. Sample SD (divide by n−1) is the right choice when your data is a sample from a larger population; population SD (divide by n) when you have the entire population. The (n−1) correction (Bessel's correction) gives an unbiased estimate of the population variance.

Frequently asked

Sample vs population — which should I use?+
Sample (n−1) for almost everything in real life. Population (n) only when you literally have every value in the population.
What is Bessel's correction?+
Dividing by n−1 instead of n. Without it, sample variance underestimates the true population variance because the sample mean is closer to the sample data than the true population mean.
How do I interpret the SD?+
For roughly normal data: ~68% of values fall within ±1 SD of the mean, ~95% within ±2 SD, ~99.7% within ±3 SD.
Why is SD better than range as a spread measure?+
SD uses every value's distance from the mean, not just the extremes. It's much less sensitive to a single outlier.
How is SD related to standard error?+
Standard error of the mean = SD / √n. SE estimates how much the sample mean would vary across different samples.

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