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Variance 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 focused on variance: paste your numbers, run it, and the variance card is highlighted among the results, next to the standard deviation, mean, standard error and coefficient of variation from the same input.

Variance is the average squared distance from the mean. Two passes compute it exactly: first x̄ = Σxᵢ ÷ n, then Σ(xᵢ − x̄)², divided by n − 1 for a sample or by n for a population. For 2, 4, 4, 4, 5, 5, 7, 9 the squared deviations sum to 32, so the population variance is 32 ÷ 8 = 4 and the sample variance is 32 ÷ 7 ≈ 4.5714.

Because squaring makes its unit the square of the data's unit (dollars², cm²), variance is mostly a stepping stone: its square root — the standard deviation — is the readable spread. The step table under the results shows every xᵢ − x̄ and its square, so you can trace exactly how the variance was built from your list.

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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.