Kurtosis Calculator

This kurtosis calculator works out the excess kurtosis of any data set, a statistic that tells you how heavy or light the tails of your distribution are compared with a normal (bell curve) distribution, and therefore how likely extreme values are to turn up. Type or paste your numbers into the data set field as a comma separated list, and the calculator instantly returns three figures: the excess kurtosis itself, the mean of your data, and the sample size it used. Excess kurtosis reads as zero for a perfectly normal distribution. A positive result, called leptokurtic, means your data has heavier tails and more outliers than normal, so extreme values are more likely than a bell curve would suggest. A negative result, called platykurtic, means lighter tails and a flatter, more evenly spread shape, with fewer extreme outliers. This matters most in finance, where heavy tails signal higher risk of large losses or gains, and in quality control and research, where it flags whether a process or sample behaves as expected or throws up unusually frequent extremes. Enter at least two values to get a result; the calculator recalculates live as you edit the list. Below you will find the underlying formula, a worked example, and answers to common questions about what the result means.

Data set, comma separated

Excess kurtosis = -1.3

Mean6

Sample size5

The formula

Excess kurtosis is the fourth standardised moment minus 3: the average of (x minus the mean) to the fourth, divided by the variance squared, then minus 3. The minus 3 makes a normal distribution read as 0.

Worked example

The set 2, 4, 6, 8, 10 has variance 8 and an excess kurtosis of minus 1.3, a flat (platykurtic) shape with lighter tails than a normal distribution. Enter that set to confirm.

Frequently asked questions

What is kurtosis?

A measure of how heavy a distribution’s tails are. Excess kurtosis compares them with the normal distribution, which scores 0.

What do positive and negative values mean?

Positive (leptokurtic) means heavier tails and more outliers; negative (platykurtic) means lighter tails and a flatter peak.

Why subtract 3?

So that the normal distribution, which has a raw kurtosis of 3, reads as an excess kurtosis of 0.

Who this calculator is for

This calculator is for statistics students, researchers and analysts.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
Results are rounded for display.

Formula and sources

Related calculators

Standard Deviation Calculator: spread of data.
Z-Score Calculator: standard score.
Mean Median Mode Calculator: averages.

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