Skewness & Kurtosis Calculator
Measure the asymmetry (skewness) and tail heaviness (excess kurtosis) of any dataset — with a histogram and a smooth shape overlay so the numbers have a visual anchor.
Shape statistics explained, step by step
This tool reports two sample moments — Fisher–Pearson adjusted skewness (G₁) and excess kurtosis (G₂). Each card below covers one piece of what the calculator actually computes.
1. Skewness — asymmetry of the distribution
Skewness measures how lopsided a distribution is. Symmetric data (like a normal curve) has skewness near 0. A long right tail gives positive skew; a long left tail gives negative skew. The tail pulls the mean toward itself, so mean vs median already hints at direction.
2. Kurtosis — tail heaviness vs a normal curve
Kurtosis is about the tails, not the peak's height. Excess kurtosis subtracts 3 so a normal distribution reads 0. Positive (leptokurtic) means fat tails and frequent extreme values; negative (platykurtic) means light tails and values cluster more evenly.
3. Plain-language classification
The calculator turns the raw numbers into a label so results are easier to read. Skew is grouped as approximately symmetric, moderately skewed, or highly skewed; kurtosis is grouped as platykurtic, mesokurtic, or leptokurtic.
4. Sample-size caveats and outlier sensitivity
Deviations are cubed for skewness and raised to the fourth power for kurtosis, so a single outlier can dominate the result. With fewer than ~30 values the estimates are noisy — treat them as rough shape indicators, and always cross-check with the Outlier Detector when values look extreme.
Features of this calculator
- Sample skewness using the Fisher–Pearson adjusted G₁ formula
- Sample excess kurtosis (G₂) — normal distribution = 0
- Automatic plain-language classification (symmetric, right/left-skewed, leptokurtic, platykurtic)
- Histogram of your data with a smooth distribution-shape overlay
- Full step-by-step working: mean, standard deviation, and formula substitution
- Robust input parser — commas, spaces, tabs, currency symbols and thousand separators
- Copy the summary or download the whole result panel as an image
Frequently asked questions
+What does 'excess' kurtosis mean?
Kurtosis is often reported relative to the normal distribution, whose kurtosis value is 3. Excess kurtosis subtracts that 3, so a normal distribution has excess kurtosis of 0. Positive means heavier tails and a sharper peak than normal (leptokurtic); negative means lighter tails and a flatter peak (platykurtic). This calculator reports excess kurtosis.
+How does skewness relate to outliers?
Skewness depends on the cube of each deviation, so a single extreme value on one side can push skewness sharply positive or negative. If a dataset has strong skew, check for outliers with the Outlier Detector before drawing conclusions.
+What sample size do I need?
Skewness needs at least 3 values and excess kurtosis needs at least 4, but both estimates are unstable with small samples. With fewer than ~30 values the numbers swing wildly from sample to sample — treat them as rough shape indicators, not precise population parameters.
+How do I interpret the skewness value?
Rough guide: |skew| < 0.5 is approximately symmetric, 0.5–1 is moderately skewed, and above 1 is highly skewed. Positive = long right tail (mean > median); negative = long left tail.