What is excess kurtosis?

Excess kurtosis (Fisher kurtosis) equals the standard kurtosis minus 3. This shifts the reference point so that a normal distribution has an excess kurtosis of exactly 0, making it easier to see departures from normality.

What does a positive excess kurtosis mean?

A positive value means the distribution is leptokurtic — it has heavier tails and a sharper peak than a normal distribution. Extreme values (outliers) occur more often than expected.

What does a negative excess kurtosis mean?

A negative value means the distribution is platykurtic — it has lighter tails and a flatter peak than a normal distribution. Extreme values occur less often than expected.

How many data points do I need?

You need at least 4 data points for a meaningful kurtosis estimate. With fewer than 4 points, the fourth central moment cannot be reliably estimated.

Does this use population or sample kurtosis?

This calculator provides both. The population formula divides by N, while the sample (bias-corrected) formula uses the adjustment factor n(n+1)/[(n-1)(n-2)(n-3)] commonly used in software like Excel's KURT function.

What is the kurtosis of a normal distribution?

A normal distribution has a kurtosis of 3 (Pearson) or an excess kurtosis of 0 (Fisher). The uniform distribution has an excess kurtosis of -1.2, and a Laplace distribution has an excess kurtosis of 3.

Kurtosis Calculator

Enter a list of numbers and instantly compute kurtosis and excess kurtosis with interpretation.

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Summary

Kurtosis measures the "tailedness" of a probability distribution — how heavy or light the tails are relative to a normal distribution. This calculator computes both the standard (Pearson) kurtosis and the excess kurtosis (Fisher), which subtracts 3 so that a normal distribution has an excess kurtosis of 0. A positive excess kurtosis indicates heavier tails (leptokurtic), while a negative value indicates lighter tails (platykurtic).

How it works

Enter your dataset as comma-separated or line-separated numbers.
The calculator computes the mean and the second and fourth central moments.
Kurtosis is calculated as the fourth central moment divided by the square of the variance.
Excess kurtosis subtracts 3 from the kurtosis (Fisher definition), centering the normal distribution at 0.
Results include the distribution type (leptokurtic, mesokurtic, or platykurtic) and key summary statistics.

Use cases

Assess tail risk in financial return distributions.
Check normality assumptions before applying parametric statistical tests.
Identify outlier-prone datasets in quality control and manufacturing.
Evaluate model fit in actuarial and risk analysis work.
Explore distributional shape in academic research and data science.
Compare the tailedness of multiple datasets side by side.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu