Kurtosis Calculator

Kurtosis is a statistical measure that describes the 'tailedness' of a probability distribution — how much of the data's variance is due to extreme values (outliers) in the tails. A higher kurtosis indicates heavier tails and a sharper peak, while lower kurtosis suggests lighter tails and a flatter peak.

Excess kurtosis is kurtosis minus 3, where 3 is the kurtosis of a normal (Gaussian) distribution. This adjustment makes it easier to compare distributions to the normal distribution. A value of 0 means the distribution is normal-like (mesokurtic); positive values indicate leptokurtic (heavy-tailed) distributions; negative values indicate platykurtic (light-tailed) distributions.

Population kurtosis uses all members of a dataset and divides by n. Sample kurtosis applies a bias correction formula (similar to Excel and SPSS) intended for a subset drawn from a larger population. Use 'Sample' when your data is a sample, and 'Population' when your data represents the entire group.

These terms classify a distribution based on its excess kurtosis. Leptokurtic (excess kurtosis > 0) has heavier tails and a sharper peak than a normal distribution. Mesokurtic (excess kurtosis ≈ 0) closely resembles a normal distribution. Platykurtic (excess kurtosis < 0) has lighter tails and a flatter peak.

For population kurtosis, the formula is the average of the fourth power of deviations from the mean, divided by the fourth power of the standard deviation. For sample kurtosis, the calculator uses the bias-corrected formula that replicates Excel's KURT() function and SPSS output, which computes excess kurtosis directly.

You need at least 4 values to compute sample kurtosis (the formula requires n > 3). For population kurtosis, a minimum of 2 values is needed. This calculator supports up to 500 values.

Yes. You can paste data from Excel or Google Sheets into the input field. Values separated by commas, spaces, tabs, or new lines are all accepted. The calculator automatically parses and cleans the input.

A perfectly normal distribution has a kurtosis of 3 and an excess kurtosis of 0. In practice, values between -0.5 and +0.5 for excess kurtosis are generally considered close to normal. Larger deviations from zero suggest the distribution has notably heavier or lighter tails than normal.