Skewness Calculator
Adjusted Fisher-Pearson skewness of a data set, with a plain read of the shape.
What it does
Skewness describes the shape of a data set rather than its average. Two sets can share the same mean and spread yet look very different, one balanced around the middle and the other dragged to one side by a few extreme values. Skewness puts a number on that lean.
The tool above takes a list of numbers and returns the sample skewness, a plain shape label, and the sample size. It uses the adjusted Fisher-Pearson form, the version most statistics texts treat as the sample skewness because it corrects for the small sample bias in the simpler formula.
A positive value points to a longer right tail, produced by a handful of large values pulling the mean above the median. Income is a classic case, where a few very high earners stretch the right side. A negative value points to a longer left tail, as with a test most people pass and a small group fails badly.
The size of the number matters as much as the sign. Values near zero suggest a roughly symmetric shape. Around plus or minus half a unit the skew is moderate, and beyond plus or minus one it is large. The tool prints a three decimal figure so you can judge the direction and grade the strength together.
Skewness is a summary, so pair it with a histogram or a box plot. A single outlying value can dominate the number, and small samples are noisy. For a fuller picture, look at the standard deviation for spread and kurtosis for tail weight alongside the skew.
How to use
- Type or paste your numbers, separated by commas or spaces.
- Use at least three values, since the formula needs a spread to divide by.
- Press calculate to see the skewness and shape.
- Read the sign first, then the size of the number.
- Plot the data to confirm what the number suggests.
- Compare with the mean and median to sense the pull.
Formula
- n
- Number of values in the sample.
- m2
- Second central moment, the average squared deviation.
- m3
- Third central moment, the average cubed deviation.
- G1
- Adjusted Fisher-Pearson sample skewness.
The central moments divide by n, and the correction term sqrt(n (n - 1)) / (n - 2) scales the raw value up for small samples. With at least three values, a mean and a nonzero spread are required, so a list of identical numbers has no defined skewness.
Worked example
Example: 2, 4, 4, 4, 5, 5, 7, 9
Eight values: 2, 4, 4, 4, 5, 5, 7, 9.
- The mean is 5.0.
- The average squared deviation, m2, is 4.0.
- The average cubed deviation, m3, is 1.5.
- The raw ratio m3 / m2^1.5 = 0.1875.
- The size correction with n = 8 raises it to 0.818.
- A positive 0.818 means a moderately right skewed sample.
Reference table
| Value | Shape | What it means |
|---|---|---|
| Below about -1 | Strong left skew | Long left tail |
| -1 to -0.5 | Moderate left skew | Slight pull to the left |
| -0.5 to 0.5 | Roughly symmetric | Balanced both sides |
| 0.5 to 1 | Moderate right skew | Slight pull to the right |
| Above about 1 | Strong right skew | Long right tail |
Limits
- Needs at least three values, more if the data are noisy.
- One extreme value can dominate the result.
- Only describes the third moment, so it ignores tail weight.
- There is no single cutoff. Read the sign and size together.
Common mistakes
- Running the calculation on fewer than three values.
- Treating any positive number as heavily skewed.
- Ignoring outliers that drive the number.
- Confusing skewness with spread, which is the standard deviation.
- Reporting three decimals as if they were precise for a tiny sample.
Try it yourself
Quick checks. Answers sit tucked under each question.
Skewness of 1, 2, 3, 4, 5?
0.000, because the set is symmetric.
Skewness of 2, 4, 4, 4, 5, 5, 7, 9?
0.818, a moderate right skew.
Why is a set of identical numbers undefined?
The spread is zero, so the formula would divide by zero.
Questions
What does a positive skewness mean?
A longer right tail, usually from a few large values pulling the mean up.
What is a good skewness value?
Near zero for typical parametric work. Between minus 1 and plus 1 is often treated as acceptable.
Which skewness does this use?
The adjusted Fisher-Pearson sample skewness, often written G1.
How many values do I need?
At least three, and more for a stable estimate.
Is skewness the same as kurtosis?
No. Skewness measures the lean and kurtosis measures the tail weight.
Why do the decimals look long?
The formula is exact, but the extra digits are not meaningful for small samples.