Skewness Calculator

Skewness measures the asymmetry of a probability distribution around its mean. A skewness of 0 indicates a perfectly symmetric distribution. Positive skewness means the tail is longer on the right side, while negative skewness means the tail is longer on the left.

A positive skewness (right-skewed) indicates that most data values are concentrated on the left with a long tail to the right. A negative skewness (left-skewed) means most values cluster on the right with a long tail to the left. Values between -0.5 and 0.5 are generally considered approximately symmetric.

This calculator uses the adjusted Fisher-Pearson standardized moment coefficient: skewness = [n / ((n-1)(n-2))] × Σ[(xi − x̄) / s]³, where n is the sample size, x̄ is the mean, and s is the sample standard deviation. This is the same formula used by Excel's SKEW function.

Kurtosis measures the 'tailedness' or peakedness of a distribution. Excess kurtosis subtracts 3 from the raw kurtosis value so that a normal distribution has an excess kurtosis of 0. Positive excess kurtosis (leptokurtic) indicates heavier tails, while negative excess kurtosis (platykurtic) indicates lighter tails than a normal distribution.

You need at least 3 data points to compute the sample skewness (since the formula divides by n−2). More data points generally yield more reliable and stable estimates of the true population skewness.

As a rule of thumb: values between −0.5 and 0.5 indicate near-symmetry; values between ±0.5 and ±1.0 indicate moderate skewness; and values beyond ±1.0 indicate high skewness. In practice, the significance depends on your sample size and the context of your analysis.

This calculator computes sample skewness using the bias-corrected formula suitable for sample data. Population skewness uses a slightly different formula (without the n/((n-1)(n-2)) correction factor). For large samples, the difference between the two is negligible.

A perfectly normal (Gaussian) distribution has a skewness of exactly 0 (perfectly symmetric) and an excess kurtosis of exactly 0. Real-world data rarely achieves these exact values, but values close to 0 suggest the data is approximately normally distributed.