Kurtosis Calculator

Measure the “tailedness” of your data with the sample and population excess kurtosis. See whether your distribution is leptokurtic, platykurtic, or close to normal.

Tested against reference valuesLast reviewed August 2026

Your data

Decimals

Excess kurtosis (sample)2.9864

leptokurtic — heavier tails and a sharper peak than normal

Population excess kurtosis: 1.1438
Skewness (sample): 1.4846
Mean (x̄): 6.1000
Std. deviation: 2.5144

Excess kurtosis is measured relative to the normal distribution (0). Add 3 for the “raw” kurtosis.

Distribution

n = 10

Frequency ±1 SDx̄

How to use this calculator

Enter your numbers, separated by commas, spaces, or new lines (at least four values).
Read the sample excess kurtosis with a plain-language interpretation.
Compare it to the population value and the skewness shown below.

What is kurtosis?

Kurtosis describes the shape of a distribution’s tails relative to a normal distribution. High kurtosis means heavy tails and more outliers; low kurtosis means light tails and fewer outliers. It is usually reported as excess kurtosis, which subtracts 3 so that a normal distribution has a value of 0.

Leptokurtic (excess > 0) — heavy tails, sharper peak, more outliers than normal.
Mesokurtic (excess ≈ 0) — tails similar to the normal distribution.
Platykurtic (excess < 0) — light tails, flatter peak, fewer outliers than normal.

Kurtosis formula

The population excess kurtosis uses the fourth standardized moment minus 3:

\text{Kurt}=\dfrac{\frac{1}{n}\sum (x_i-\bar{x})^4}{\left[\frac{1}{n}\sum (x_i-\bar{x})^2\right]^2}-3

The sample excess kurtosis applies a bias correction (this is what Excel’s KURT returns):

G_2=\dfrac{n(n+1)}{(n-1)(n-2)(n-3)}\sum \left(\dfrac{x_i-\bar{x}}{s}\right)^4-\dfrac{3(n-1)^2}{(n-2)(n-3)}

Kurtosis in Excel

Use =KURT(range) to get the sample excess kurtosis. Excel returns the bias-corrected value (G₂), where a normal distribution gives approximately 0.

Frequently asked questions

What is excess kurtosis?

Excess kurtosis is the kurtosis minus 3, so that the normal distribution has a value of 0. Positive excess kurtosis means heavier tails than normal (leptokurtic); negative means lighter tails (platykurtic).

What does high kurtosis mean?

High (positive excess) kurtosis means the distribution has heavier tails and a sharper peak than a normal distribution, so extreme values or outliers are more likely.

What is the difference between skewness and kurtosis?

Skewness measures the asymmetry of a distribution, while kurtosis measures the heaviness of its tails. A distribution can be symmetric (zero skew) yet still have high or low kurtosis.

How do I calculate kurtosis in Excel?

Use =KURT(range), which returns the sample excess kurtosis with the normal distribution as the zero baseline.

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