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Skewness Calculator

Enter your numbers to compute the skewness of the distribution.

How it is calculated

Paste your numbers separated by spaces, commas, semicolons or line breaks (at least 3 values). The tool computes the mean, the population standard deviation, and two skewness values from the central moments m2 = Σ(x − mean)² / n and m3 = Σ(x − mean)³ / n:

g1 = m3 / m21.5 (population skewness) and G1 = g1 × √(n(n − 1)) / (n − 2) (sample, adjusted Fisher-Pearson)

Positive means a longer right tail, negative a longer left tail, and values near 0 mean roughly symmetric. If all values are identical, or any entry is not a number, no result is shown. Results are rounded to four decimals.

Worked example

Data: 2, 3, 3, 4, 5, 6, 12 (n = 7). The mean is 35 / 7 = 5.0000. Deviations are −3, −2, −2, −1, 0, 1, 7; their squares sum to 68, so m2 = 9.714 and the population SD is 3.1168. Their cubes sum to 300, so m3 = 42.857 and g1 = 42.857 / 9.7141.5 = 1.4155. The sample correction multiplies by √42 / 5 = 1.296, giving G1 = 1.8347. The large positive value reflects the single high value, 12, pulling the right tail out.

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Common mistakes

  • Using a decimal comma such as 3,5 in the list. Commas separate values here, so it is read as two numbers, 3 and 5; write 3.5.
  • Quoting the population value (g1) when a textbook or software reports the sample one (G1); the two differ noticeably for small n.
  • Reading a skewness near zero as proof of a normal distribution; a symmetric distribution can still have heavy tails or two peaks.
  • Judging skewness from a handful of points. With 3 to 5 values the figure swings widely, and one outlier can dominate it.
  • Mixing units or leaving a stray text label in the data, which makes the whole input invalid.

About this calculator

Skewness measures how asymmetric a distribution is around its mean. The population skewness uses the third standardized moment (average of the cubed deviations from the mean, divided by the cubed standard deviation), while the sample skewness applies the Fisher-Pearson adjusted G₁ correction to reduce bias from working with a limited sample instead of the full population. A positive value means a longer right tail, negative means a longer left tail, and zero matches a symmetric distribution like the normal curve.

Data analysts and quants check skewness before applying statistical tests or models that assume normality, deciding whether a transform (like a log transform) is needed first, while quality engineers use it to spot asymmetric variation in a manufacturing process that a simple mean and standard deviation would miss.

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Comments (1)

  • Editorial team

    A practical use is deciding whether to transform data. If the skewness is strongly positive and every value is above zero, take the logarithm of each value, paste those back in and compare: a clear drop toward zero suggests a log scale fits better. The tool shows the mean and the population standard deviation but no median, so compare the mean with the median yourself. What kind of data are you checking?

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