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Sample Skewness from Third Moment and Variance Calculator

g₁ = m₃ / σ³ = m₃ / Var^(3/2).

Compute the sample skewness — the third standardized moment of a distribution — from the centred third moment m₃ = E[(X − μ)³] and the variance σ² = E[(X − μ)²]: g₁ = m₃ / σ³ = m₃ / Var^(3/2). g₁ = 0 for symmetric; > 0 means right tail heavier; < 0 means left tail heavier.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

g₁ = m₃ / σ³.

In depth

Compute the sample skewness — the third standardized moment of a distribution — from the centred third moment m₃ = E[(X − μ)³] and the variance σ² = E[(X − μ)²]: g₁ = m₃ / σ³ = m₃ / Var^(3/2). g₁ = 0 for symmetric; > 0 means right tail heavier; < 0 means left tail heavier.