Unit Converters · Free tool
Standard Deviation Calculator
Calculate sample (n−1) and population (n) standard deviation and variance side by side. Paste any list of numbers. Free, instant, browser-only, no sign-up.
n
8
Mean (x̄)
23.125
Min / Max
12 / 34
Range
22
Sample (divide by n−1)
σ ≈ 7.7908
Variance: 60.6964
Use when your data is a subset of a larger population.
Population (divide by n)
σ = 7.2876
Variance: 53.1094
Use only when you have the entire population — rare in real research.
Why two different formulas
Sample variance divides by n − 1 (Bessel's correction) because the sample mean is itself an estimate — it slightly underestimates the true population variance, so you compensate by using a smaller divisor.
For most inferential work (hypothesis tests, confidence intervals), use the sample formula. The population formula is only correct when your data is literally the entire population — e.g. every student in a 30-person class.
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What it does
Compute mean, variance, and standard deviation for any list of numbers — with both the sample (n−1) and population (n) formulas shown side-by-side, so students can pick the right one for their assignment without second-guessing.
For a full summary including median, mode, and range see the average calculator. To check whether your variance is significant, use the p-value calculator.
Embed this tool on your siteShow snippetHide
Paste this snippet into any page. Loads on-demand (lazy), no tracking scripts, and sized to most dashboards. Replace the height to fit your layout.
<iframe src="https://freetoolarena.com/embed/standard-deviation-calculator" width="100%" height="720" frameborder="0" loading="lazy" title="Standard Deviation Calculator" style="border:1px solid #e2e8f0;border-radius:12px;max-width:720px;"></iframe>How to use it
- Paste your numbers — comma, space, or newline separated.
- Read the sample (n−1) standard deviation for inferential work.
- Use the population (n) version only if you have the entire population.
- Variance is the squared standard deviation — both are shown.
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