A walkthrough, end to end.
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Paste or type your numbers separated by commas, spaces, or newlines.
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The calculator returns both population (σ) and sample (s) standard deviation, with variance.
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Population: divide by n. Sample (Bessel's correction): divide by n−1.
Standard deviation
Measures spread of data around the mean. Population SD divides by n; sample SD divides by n−1 (Bessel's correction) to better estimate the true population SD from a sample.
What you can do with this.
Test scores spread
Two classes with same mean but very different SDs: low SD = consistent students; high SD = some excelling, some struggling. Tells the teacher more than mean alone.
Quality control
Manufacturing tolerance: lower SD means more consistent product. Six Sigma quality targets ±6 SDs from mean for defect rate < 3.4 per million.
Investment volatility
Stock returns standard deviation = volatility. Higher SD = bumpier ride. Used in Sharpe ratio (risk-adjusted return) and most modern portfolio theory.
Population vs. sample
Use population SD (σ) when you have ALL the data. Use sample SD (s) when your data is a subset and you're estimating the population. The calculator gives both — pick the right one for context.
Empirical rule (68-95-99.7)
For roughly normal data: 68% within 1 SD, 95% within 2 SDs, 99.7% within 3 SDs. The calculator's mean and SD let you sanity-check distribution assumptions.
Z-score calculation
z = (value − mean) / SD. Tells you how many SDs from mean. The Z-score Calculator handles the next step; the SD is one of the inputs.
Coefficient of variation
CV = SD / mean × 100%. Dimensionless way to compare variability across different scales (e.g., comparing variability of small vs. large numbers).
Standard deviation 2026 — what's current
Foundation of statistics; unchanged. Spreadsheets use STDEV.S (sample, default in modern Excel) and STDEV.P (population). Match your formula to your context — sample is the most common default.
Frequently asked.
If your data IS the entire population (e.g., all employees at a company), use population. If your data is a subset (e.g., random sample of 100 customers), use sample. When in doubt, use sample.
Bessel's correction. Using n underestimates the true population SD when working from a sample. Dividing by n−1 corrects this bias.
SD squared. Variance has units squared (e.g., dollars²); SD has the original units. SD is more interpretable; variance is preferred for some statistical operations.
No. Calculations run entirely in your browser.