Skewness Calculator

Calculate population Fisher–Pearson skewness g1 and adjusted sample skewness G1; requires at least three values and non-zero spread.

The Skewness Calculator reports two third-moment statistics: population Fisher–Pearson skewness g1 and adjusted sample skewness G1, using the correction associated with Excel SKEW. It requires at least three accepted finite values and non-zero spread. When those conditions are not met, the page shows a validation message instead of an undefined numeric result.

The population coefficient summarizes the signed third central moment relative to the standard deviation cubed. Its sign describes the direction of the third-moment asymmetry, while its magnitude depends on the entire dataset and can be influenced by extreme observations. The adjusted value applies a finite-sample correction; it is not a different input dataset.

The input accepts comma or whitespace separators and displays malformed or non-finite tokens as ignored. Both outputs use exactly the accepted list. Skewness is dimensionless because deviations are standardized, but a dimensionless value is not automatically comparable across studies unless data definitions and calculation conventions match.

For a separate fourth-moment shape summary, see the Kurtosis Calculator; pair shape with the centre from the Mean Calculator.

Enter at least three finite numeric observations measured on one consistent scale.
Confirm the ignored-token list is empty or that every listed exclusion is intentional.
Check that the accepted values are not all identical; zero spread makes skewness undefined.
Read g1 as the population Fisher–Pearson coefficient and G1 as the adjusted sample estimate associated with Excel SKEW.
Use the sign as a description of third-moment direction, not as a normality test or a causal explanation.

Population and adjusted Fisher–Pearson skewness

Let m₂ = Σ(xᵢ − x̄)² / n and m₃ = Σ(xᵢ − x̄)³ / n. Population Fisher–Pearson skewness is g1 = m₃ / m₂^(3/2), provided m₂ is greater than zero.

The adjusted sample value is G1 = √[n(n − 1)] / (n − 2) × g1. It is defined here only for n ≥ 3 and non-zero spread. The factor adjusts the population moment coefficient for sample size; it does not make the input representative or remove outlier influence.

Because numerator and denominator scale together, skewness has no measurement unit. The page computes a descriptive coefficient only. It does not calculate a standard error, confidence interval, p-value, or formal test of symmetry.

Reading g1 and adjusted G1

Two coefficients, one accepted dataset

The first row is population Fisher–Pearson g1. The second is adjusted G1, labelled with Excel SKEW to identify the sample correction. With the same observations, the two can differ because the adjustment depends on n. Neither value reports a probability that the data are skewed.

For the default six values, g1 is approximately 0.9075 and adjusted G1 is approximately 1.2426. The positive sign describes positive third-moment asymmetry for this list. These are descriptive results for the six numbers, not evidence about a wider population or a conclusion about why the values differ.

A zero-spread list has no defined standardized third moment because its standard deviation is zero. Lists shorter than three also cannot use the adjusted formula shown here. The calculator withholds those result rows and explains the minimum or zero-spread condition.

Adding the same constant to all values does not change either coefficient because the deviations from the mean remain the same. Multiplying every value by a positive unit-conversion factor also leaves standardized skewness unchanged: the third-moment numerator and the standard-deviation cubed denominator scale together. Reversing the direction of a measurement scale changes the sign, so the orientation of the data still matters.

The adjusted coefficient is calculated from the population coefficient and n using the displayed correction. It is not obtained by editing, winsorising, or resampling the observations. If two reports disagree, check their accepted inputs, minimum-value rules, and whether they report g1 or adjusted G1 before assuming one implementation is wrong.

Statistics tips and best practices

Keep g1 and G1 labels attached to their values; the adjustment is part of the definition.
Check extreme observations because cubed deviations can make them influential.
Use the same missing-value and inclusion rules before comparing skewness across datasets.
Treat the sign as a direction summary, not as proof of a particular distribution or mechanism.
Do not interpret the coefficient as a normality test; this page provides no test statistic or p-value.

Skewness worked example

For the default six values, the mean is 18, m₂ is 151.6667, and m₃ is 1,695.
g1 = 1,695 / 151.6667^(3/2) ≈ 0.9075.
Applying √[6 × 5] / (6 − 2) to g1 gives adjusted G1 ≈ 1.2426.

Common mistakes to avoid

Calling g1 and G1 the same estimate without noting the sample-size correction.
Treating a positive coefficient as an explanation for why the data were generated.
Assuming dimensionless means comparable even when datasets use different selection rules.
Expecting a result for fewer than three values or for a constant list.
Using skewness alone to establish normality, significance, or the presence of a particular outlier.

Skewness values are descriptive moment calculations for the accepted finite inputs. They are not a test of normality, a confidence interval, or a population-level conclusion.

For consequential analysis, check the study design, sample size, and sensitivity to extreme observations. The calculator does not validate those assumptions or provide inferential uncertainty.