basic

Sample Excess Kurtosis from 4th Moment and Variance Calculator

Excess kurtosis = m₄ / σ⁴ − 3.

Compute the excess kurtosis of a distribution from its centred fourth moment m₄ = E[(X − μ)⁴] and the variance σ²: excess_kurtosis = m₄ / σ⁴ − 3. Subtracting 3 makes a normal distribution have an excess kurtosis of 0. > 0 = leptokurtic (heavy tails); < 0 = platykurtic (light tails).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

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

γ₂ = m₄ / σ⁴ − 3.

In depth

Compute the excess kurtosis of a distribution from its centred fourth moment m₄ = E[(X − μ)⁴] and the variance σ²: excess_kurtosis = m₄ / σ⁴ − 3. Subtracting 3 makes a normal distribution have an excess kurtosis of 0. > 0 = leptokurtic (heavy tails); < 0 = platykurtic (light tails).