Enter your dataset as comma- or space-separated numbers to calculate kurtosis and excess kurtosis for your distribution. Paste values into the Data Values field, choose Sample or Population, and get back the kurtosis coefficient, excess kurtosis, skewness, mean, and standard deviation — plus a visual breakdown of your data's tail heaviness.
Kurtosis
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Excess Kurtosis
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Skewness
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Mean
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Standard Deviation
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Count (n)
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Distribution Type
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Kurtosis is a statistical measure that describes the shape of a distribution's tails relative to a normal distribution. High kurtosis means heavier tails and a sharper peak (leptokurtic), while low kurtosis indicates lighter tails and a flatter peak (platykurtic). A normal distribution has a kurtosis of 3.
Excess kurtosis is kurtosis minus 3, adjusted so that a normal distribution has a value of zero. This is the formula used by Excel and SPSS. Positive excess kurtosis indicates heavier-than-normal tails, negative excess kurtosis indicates lighter tails. When people say 'kurtosis' in practice, they often mean excess kurtosis.
Population kurtosis uses the entire dataset as the full population, dividing by n. Sample kurtosis applies a bias correction formula (using n-1 and correction factors) to better estimate the true population kurtosis from a sample. Use 'Sample' when your data is a subset of a larger population, and 'Population' when you have complete data.
A kurtosis of 3 (excess kurtosis = 0) means your distribution is mesokurtic, similar to a normal distribution. Excess kurtosis greater than 0 (leptokurtic) means the distribution has heavier tails and more extreme outliers. Excess kurtosis less than 0 (platykurtic) means lighter tails and fewer extreme values.
Skewness measures the asymmetry of a distribution — a positive skew means the tail extends more to the right, negative skew to the left. Kurtosis measures the heaviness of the tails regardless of direction. Together, skewness and kurtosis describe the overall shape of a distribution beyond just mean and standard deviation.
Most statisticians recommend at least 20 data points for a meaningful kurtosis estimate, though this calculator accepts between 5 and 500 values. With small samples, kurtosis estimates can be highly variable. For very small datasets, interpret the results with caution.
You can enter numbers separated by commas, spaces, or new lines — for example: 2, 4, 6, 8 or 2 4 6 8. You can also paste data directly from a spreadsheet. The calculator will parse any combination of these separators automatically.
A normal distribution has a kurtosis of exactly 3 (excess kurtosis = 0) and serves as the baseline reference. Many statistical tests assume normality, so comparing your data's kurtosis to 3 helps assess whether those tests are appropriate. Significant deviations from 0 excess kurtosis may indicate your data requires non-parametric methods.