How to use this kurtosis calculator
Enter your data above and press Calculate. The calculator returns the excess kurtosis: the convention used by Excel (KURT) and most software, where a normal distribution scores 0.
What kurtosis measures (and what it does not)
Kurtosis measures tail weight: how much of a distribution's action happens in its extremes rather than its shoulders. High kurtosis means outliers are a feature, not an accident. Financial returns are the textbook case. Low (negative) kurtosis means the data hugs its range evenly and extremes are rare, like the height of a doorway's daily users all being adults.
One myth to bury: kurtosis is not really about the peak. A distribution can be flat-topped and still heavy-tailed. Modern statisticians define it purely through the standardised fourth moment: it is a tail statistic, not a peak statistic.
Nine tightly-bunched values: 5, 6, 6, 7, 7, 7, 8, 8, 9 give excess kurtosis ≈ −0.75: lighter tails than a normal distribution (platykurtic), exactly what you would expect from data confined to a narrow band with no extremes at all.
Reading excess kurtosis
- Around 0: normal-like tails (mesokurtic).
- Above ~1: heavy tails (leptokurtic): expect outliers; means and standard deviations become fragile.
- Below ~−1: light tails (platykurtic): uniform-like data; extremes are rarer than normal.
Frequently asked questions
What is excess kurtosis?
Kurtosis measured relative to the normal distribution, whose kurtosis is defined as 3. Excess kurtosis subtracts the 3, so normal = 0, heavy tails are positive, light tails negative.
Is kurtosis about the peak of the distribution?
Mostly no, despite the common textbook claim. Kurtosis is driven by the tails: the presence or absence of extreme values.
Why does kurtosis matter in finance?
Asset returns have high kurtosis: crashes and rallies far beyond normal-distribution predictions happen regularly. Risk models that ignore kurtosis underestimate extreme losses.