This skewness calculator measures the asymmetry of a dataset — the Fisher–Pearson coefficient (sample-adjusted G1, as in Excel’s SKEW) with an interpretation of direction and strength.

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Sign Convention: the Sign Points at the Tail, Not the Bulk

Positive skew = long right tail (most data bunched left, like incomes); negative skew = long left tail. The quartile view of the same shape is our Five Number Summary Calculator. Part of our Statistics Calculators collection.

Worked Example (Verified)

  • 2, 3, 4, 5, 14 (defaults): mean 5.6, m₂ = 18.64, m₃ = 104.83 → g1 = 1.303, sample G1 = 1.942 — highly right-skewed; the single 14 stretches the tail and the cube in m₃ makes sure we notice
  • Income reality check: national income distributions run G1 ≈ +1 to +2 — the defaults are a five-household economy with one rich neighbor
  • Near-zero cases: heights within one sex run |G1| < 0.3 — bell-ish enough that mean and median hold hands
  • Exam-score left skew: easy tests pile scores at the top with a tail of strugglers — negative G1, mean below median

Using Skewness Well

  • Interpretation bands (rule of thumb): |G1| < 0.5 fairly symmetric; 0.5–1 moderate; > 1 high.
  • Transforms (log, sqrt) tame right skew before modeling — log-income is a near-bell.
  • Skewness says nothing about bimodality: two humps can average into perfect symmetry.
  • Report n alongside: G1’s own sampling wobble is large in small samples (SE ≈ √(6/n)).

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Frequently Asked Questions

How do you calculate skewness?

The moment coefficient g1 = m₃/m₂^1.5, where m₂ and m₃ are the second and third central moments; the sample-adjusted Fisher–Pearson G1 multiplies by √(n(n−1))/(n−2). For 2, 3, 4, 5, 14: g1 = 1.303, G1 = 1.942 — strongly right-skewed. This calculator reports G1 (the Excel/SPSS convention) and shows g1 too.

What does positive skew mean?

A long tail to the right: most values cluster low with a few large ones pulling the mean up (mean > median). Incomes, house prices, city sizes and reaction times live here. Negative skew mirrors it — pile-up high, tail low, mean < median.

What skewness is acceptable?

Rules of thumb: |G1| under 0.5 reads as fairly symmetric; many applied fields treat |G1| under 2 (with kurtosis checks) as workable for normal-theory methods at moderate n. It’s a guideline, not a law — robust methods and transforms exist precisely for the cases outside.

Can skewness be zero for non-symmetric data?

Yes — asymmetry in opposite directions can cancel in the third moment, and bimodal symmetric data also score zero. Skewness is one lens (asymmetry), not a normality certificate; pair it with a plot and the five-number summary.

Why do packages report different skewness for the same data?

Two formulas circulate: the raw moment ratio g1 and the sample-adjusted G1. At n = 5 they differ hugely (1.303 vs 1.942); at n = 500 they’re nearly twins. Know which your tool prints — this page prints both and labels them.

Is this skewness calculator free?

Yes — free, instant, no sign-up.