Skewness Calculator
Whether your data leans left or right — the third moment, with the sample-adjusted G₁ statistic and a plain reading of what it means.
Skewness is the average cubed z-score.
How the skewness calculator works
Skewness is the average cubed z-score. Cubing preserves sign, so values far above the mean contribute positively and those far below negatively; a symmetric distribution cancels to zero.
The calculator reports the adjusted Fisher–Pearson coefficient G₁ that Excel and most software use, which corrects the bias in small samples, alongside the simpler population version.
Formula: g₁ = (1/n) Σ((xᵢ − x̄)/σ)³; G₁ = g₁ √(n(n−1)) / (n−2)
Worked examples
| Inputs | Skewness (G₁, sample) | Note |
|---|---|---|
| A right-skewed set | 2.07044 | positive skew — mean above median |
| Symmetric | 0 | skewness 0 |
| Left-skewed | -1.714169 | negative skew |
FAQFrequently asked questions
What does positive skewness mean?
A long tail on the right: most values cluster low with a few large ones. Income and house prices are the classic examples.
How big is a big skew?
Under 0.5 is roughly symmetric; over 1 is substantial. Dividing by the standard error gives a z-score you can test.
Does the mean or the median sit higher?
In right-skewed data the mean is pulled above the median by the tail; in left-skewed data it falls below.
Why is skewness cubed?
Because an odd power keeps the sign, so deviations above and below the mean do not cancel out the way they would if squared.
What should I do about a skewed variable?
Often a log transform makes it approximately symmetric, which is why so much financial and biological analysis is done in logs.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.