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Sample Standard Deviation Calculator

Paste your numbers and get the sample or population standard deviation, variance, mean, SEM and CV% — with the squared deviations shown step by step.

Separate numbers with commas, spaces or new lines. A decimal comma like 3,14 is understood — separate such numbers with spaces or new lines.

Processing... 0%
Parsing the numbers
Computing the mean
Summing the squared deviations

Result

This page opens the standard deviation calculator preset to the sample formula: paste your numbers, run it, and you get the sample standard deviation s together with the variance, mean, standard error and coefficient of variation — plus the full deviations table.

The sample formula divides the sum of squared deviations by n − 1 instead of n: s = √(Σ(xᵢ − x̄)² ÷ (n − 1)). This is Bessel's correction — because the mean was estimated from the same data, the raw deviations are slightly too small on average, and dividing by n − 1 compensates. For 2, 4, 4, 4, 5, 5, 7, 9 that gives √(32 ÷ 7) ≈ 2.1381.

Use the sample formula whenever your numbers are a subset standing in for something bigger: survey responses, a batch of test measurements, a week of response times sampled from a year. If your data is the entire population, switch the select to population mode — with the same input you can compare both divisors instantly.

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Accepted Formats & Rules

  • Standard deviation, variance, mean, standard error of the mean (SEM) and coefficient of variation (CV%).
  • Exact two-pass algorithm: the mean first, then the true squared deviations — no streaming shortcuts.
  • Step-by-step deviations table (first 50 rows for long lists, with sums always covering every value).

Key Benefits

✓ Sample (n − 1) and population (n) formulas in one tool — pick the right one with a single select.
✓ The full working is shown: every deviation from the mean, its square, and the exact sums used.
✓ Everything is computed locally in your browser — your data never leaves the page.

Use Cases

  • • Paste a batch of lab or QA measurements and get the sample standard deviation with Bessel's correction (n − 1), ready to quote in a report.
  • • Compare volatility between two data sets — response times, prices, test scores — using the coefficient of variation, which normalizes SD by the mean.
  • • Hand-check homework: the step table prints every xᵢ − x̄ and (xᵢ − x̄)² so each squared deviation can be verified line by line.