Statistics
Skewness and Kurtosis Calculator
Paste your data to get skewness (which way and how strongly the distribution leans) and kurtosis (how heavy the tails are). mathcheck shows the population versions built from central moments and the bias-adjusted sample versions that Excel's SKEW and KURT report, along with the moments themselves and an interpretation.
At least 4 values (sample kurtosis needs n ≥ 4).
Try an example
Result
Sample skewness (G1)
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- Population skewness (g1)
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- Sample excess kurtosis (G2)
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- Population kurtosis (m4/m2²)
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- Population excess kurtosis
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- Shape
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- Mean
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More details (1 more)
- Median
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the skewness and kurtosis calculator solves
Paste your data to get skewness (which way and how strongly the distribution leans) and kurtosis (how heavy the tails are). mathcheck shows the Every member of the group you actually care about, not just the ones measured. versions built from central moments and the bias-adjusted A smaller group taken from a population, used to estimate facts about the whole group. versions that Excel's SKEW and KURT report, along with the moments themselves and an interpretation.
Formula
How to use it
- Paste at least four data values.
- Read the sample skewness (the headline number, matching Excel SKEW) and the sample excess kurtosis (matching Excel KURT).
- Use the population versions when the data is the whole population or when a textbook uses the moment formulas.
- Check the shape sentence and the mean-vs-median line for a plain-English reading.
How to read the answer
Skewness near 0 means symmetric; positive means a long right tail with the mean pulled above the median; negative means the opposite. As a rough guide, |skewness| under 0.5 is roughly symmetric, 0.5 to 1 moderate, above 1 strong. Excess kurtosis near 0 matches a normal distribution; positive values mean heavier tails and more outliers than a normal, negative values mean lighter tails. Kurtosis is about tails, not about how peaked the middle looks.
Common mistakes and edge cases
- Mixing up kurtosis (normal = 3) with excess kurtosis (normal = 0); Excel and SPSS report excess kurtosis.
- Comparing a sample-adjusted value with a population value; for small n they differ noticeably.
- Reading skewness as a measure of spread; it describes asymmetry only.
- Trusting kurtosis from a handful of points; the fourth power makes it extremely sensitive to single extreme values.
Worked examples
Right-skewed data
Sample skewness (G1)
1.5374
Symmetric data
1 through 9 has zero skewness
Sample skewness (G1)
0
Left-skewed data
Sample skewness (G1)
-2.3853
Negative and decimal values
Sample skewness (G1)
1.2304
Heavy-tailed data
One extreme value on each side
Sample skewness (G1)
0
Undefined: identical values
Sample skewness (G1)
Error
Frequently asked questions
What is a good skewness value?+
Values between -0.5 and 0.5 are usually treated as roughly symmetric, -1 to -0.5 or 0.5 to 1 as moderately skewed, and beyond ±1 as highly skewed. The sign tells you which tail is longer.
What does kurtosis measure?+
The weight of the tails relative to a normal distribution. Positive excess kurtosis means more extreme values than a normal with the same variance; negative means fewer. It is not a measure of how peaked the center is.
Why does Excel's SKEW differ from the moment formula?+
Excel and SPSS apply a small-sample correction: G1 = g1 × √(n(n - 1))/(n - 2). This calculator reports both so you can match either source.
What is excess kurtosis?+
Kurtosis minus 3, so that a normal distribution scores 0. Software almost always reports excess kurtosis under the name kurtosis.
How are skewness and the mean-median relationship connected?+
With a long right tail the mean is pulled above the median, so positive skew usually means mean > median; negative skew usually means mean < median. The rule has exceptions for multimodal or discrete data.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026