Skewness & Kurtosis Calculator

Measure the asymmetry and tail weight of a data set, with the sample formulas used by Excel and most statistics software.

Your data

8 values read. Separate with commas, spaces, or new lines.

Skewness (G₁)

2.8035

Excess kurtosis (G₂)

7.8949

The data are highly skewed to the right (positive) (mean 11.375 vs. median 7). Excess kurtosis of 7.89 means the tails are heavier than a normal distribution's. Skewness is 3.73 times its standard error (0.752); a ratio beyond about ±2 suggests the skew is unlikely to be chance alone.

Sample skewness G₁ (Excel SKEW)	2.80347
Population-style skewness g₁	2.24778
Sample excess kurtosis G₂ (Excel KURT)	7.89486
Population-style excess kurtosis g₂	3.09279
Standard error of skewness	0.7521
Standard error of kurtosis	1.48088
Mean / median / standard deviation	11.375 / 7 / 13.617

G₁ = [n ÷ ((n−1)(n−2))] × Σ[(xᵢ−x̄)/s]³; G₂ = [n(n+1) ÷ ((n−1)(n−2)(n−3))] × Σ[(xᵢ−x̄)/s]⁴ − 3(n−1)² ÷ ((n−2)(n−3))

How to use this tool

Paste your data, separated by commas, spaces, or new lines. At least four values are needed.
Read the sample skewness G₁ and the sample excess kurtosis G₂.
Use the plain-language summary and the standard errors to judge whether the shape differs from a normal distribution.
Compare with the mean and median: right skew pulls the mean above the median.

Formula Reference

Sample skewness G₁

[n ÷ ((n−1)(n−2))] × Σ[(xᵢ−x̄)/s]³

Sample excess kurtosis G₂

[n(n+1) ÷ ((n−1)(n−2)(n−3))] × Σ[(xᵢ−x̄)/s]⁴ − 3(n−1)² ÷ ((n−2)(n−3))

SE of skewness

√[ 6n(n−1) ÷ ((n−2)(n+1)(n+3)) ]

ArticleSkewness and Kurtosis ArticleExploratory Data Analysis ArticleQ-Q Plots CalcDescriptive Statistics Calculator ToolHistogram Maker GlossaryGlossary: Skewness

Frequently Asked Questions

What is a good skewness value?+

A symmetric distribution has skewness near 0. As a rough guide, values between −0.5 and 0.5 are approximately symmetric, values from 0.5 to 1 in either direction are moderately skewed, and values beyond 1 are highly skewed.

What does excess kurtosis mean?+

Kurtosis measures how heavy the tails are. Excess kurtosis subtracts 3, the value for a normal distribution, so a normal distribution scores 0. Positive values mean heavier tails and more outlier-prone data; negative values mean lighter tails.

Why are there two versions of each statistic?+

The population-style formulas (g₁, g₂) use the simple moments of the data. The sample versions (G₁, G₂) apply a small-sample adjustment and are what Excel’s SKEW and KURT functions return. They converge as n grows.

Can a single outlier change the result?+

Yes, dramatically. Skewness and kurtosis are built from third and fourth powers of deviations, so extreme values dominate. Always look at a histogram or box plot alongside the numbers.

How to use this tool

Paste your data, separated by commas, spaces, or new lines. At least four values are needed.

Read the sample skewness G₁ and the sample excess kurtosis G₂.

Use the plain-language summary and the standard errors to judge whether the shape differs from a normal distribution.

Compare with the mean and median: right skew pulls the mean above the median.