Skewness Calculator — Distribution Shape

Skewness tells you which direction a distribution leans. Positive skew (right tail longer) pulls the mean above the median – common in income data, reaction times, and prices. Negative skew (left tail longer) pushes the mean below the median – seen in age-of-death in developed countries and scores on easy exams.

The formula used here is the Fisher-Pearson standardized moment:

g1 = [sum((xi - x-bar)^3) / n] / sigma^3

where sigma is the population standard deviation. As a rough guide: |g1| below 0.5 is approximately symmetric. Between 0.5 and 1 is moderately skewed. Above 1 is highly skewed. These thresholds appear in Bulmer’s 1965 Principles of Statistics and are widely cited, though not universal.

Note that Excel SKEW() uses a sample-adjusted version with a correction factor of n(n-1)/(n-2). For datasets of 3-8 values the difference can be meaningful – this calculator uses the population formula. For n above 30 the two converge.

This calculator also returns excess kurtosis: g2 = [sum((xi - x-bar)^4) / n] / sigma^4 - 3. A normal distribution has g2 = 0. Positive kurtosis (leptokurtic) means fatter tails and a sharper peak than normal – financial returns often show this. Negative kurtosis (platykurtic) means thinner tails and a flatter distribution.

Neither skewness nor kurtosis alone tells you the distribution is normal. That needs a Shapiro-Wilk test or similar. But together they catch most obvious departures from normality in a quick scan.

Enter at least 3 values. Blanks are skipped. Duplicate values are fine.