StatsCalculators.com

Kurtosis

The Kurtosis Calculator helps you measure the "tailedness" of your data distribution - how heavy or light the tails are compared to a normal distribution. This can reveal important patterns in your data, such as whether extreme values occur more frequently than expected. For example, in financial analysis, high kurtosis could indicate a higher risk of extreme market movements.

Quick Calculator

Need a quick calculation? Enter your numbers below:

Calculator

1. Load Your Data

Select Columns & Options

Learn More

Understanding Kurtosis

Definition

Kurtosis is a measure of the "tailedness" of a probability distribution. It quantifies how heavy the tails of a distribution are compared to a normal distribution.

Formula

Sample Kurtosis:

Kurtosis=i=1n(xixˉ)4/ns43 \text{Kurtosis} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^4 / n}{s^4} - 3

Where:

  • xix_i is each value in the sample
  • xˉ\bar x is the mean of the sample
  • nn is the number of values
  • ss is the sample standard deviation

Interpretation Guidelines

Kurtosis = 0: Normal distribution (mesokurtic)
Kurtosis > 0: Heavy-tailed distribution (leptokurtic)
Kurtosis < 0: Light-tailed distribution (platykurtic)

Visual Examples of Kurtosis

The following examples illustrate how kurtosis affects the shape of a distribution.

Mesokurtic Distribution

Kurtosis ≈ 0

Characteristics: Moderate peak height and tail weight, typical of normal distribution

Similar to normal distribution with balanced tails.

Leptokurtic Distribution

Kurtosis > 0

Characteristics: Taller peak with more concentration of data, thicker tails indicating more extreme values

Higher peak and heavier tails than normal distribution.

Platykurtic Distribution

Kurtosis < 0

Characteristics: Flatter peak with more even spread of data, thinner tails indicating fewer extreme values

Lower peak and lighter tails than normal distribution.

Related Calculators

Help us improve

Found an error or have a suggestion? Let us know!