# Kurtosis Calculator

By Scott Paulin

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Kurtosis measures how much data is in the tails of a distribution.

A distribution with large kurtosis will have "heavy tails", which means that there are a lot of outliers. A distribution with low Kurtosis is considered more "central", and will have fewer outliers.

## When To Use Kurtosis

Kurtosis is useful to measure when you want to gauge how many outliers a distribution might have. It can be used with a histogram to visualize the distribution. Skewness can be used to measure the symmetry of the distribution. A boxplot can be used to visualize the distribution's five-number summary.

## How To Calculate Kurtosis

Click the dataset input at the top of the page. Or drag and drop your dataset into the input box.

2. ### View the kurtosis of each column

A table with the kurtosis of each column will appear on the screen

## Kurtosis Formula

Kurtosis = sum(x_i - x_mean)^4 / (n * standard_deviation^4)

Where x_i is a point, x_mean is the mean of all points x, n is the number of points and standard_deviation is the standard deviation of x.

## Types of Kurtosis

The kurtosis of a set of numbers can be classified based on how it compares to the Kurtosis of the normal distribution. The normal distribution has a kurtosis of 3.

Leptokurtic distributions have a higher kurtosis than the normal distribution. These distributions have long, heavy tails. Sometimes Leptokurtic distributions are said to have positive, excess kurtosis. Mesokurtic distributions have a kurtosis of 3. Platykurtic datasets have a kurtosis of less than 3. ## Excess Kurtosis

Excess kurtosis is used to compare the kurtosis of a distribution with the normal distribution.

Excess kurtosis = kurtosis - 3

Where kurtosis is the kurtosis of your dataset.

Leptokurtic distributions have a positive excess kurtosis, while platykurtic distributions have a negative excess kurtosis.

You can calculate excess kurtosis by using the kurtosis calculator and subtracting 3 from the result.