Skewness Calculator

About the Skewness Calculator

The skewness calculator measures how asymmetric a dataset's distribution is, showing whether values trail off more toward the high end, the low end, or spread out evenly around the center. It uses the adjusted Fisher-Pearson sample skewness formula, the version built to work reasonably well on real, limited samples rather than only on very large ones. Enter a list of numbers to get both the skewness value and a plain-language shape label.

How It Works

Enter your numbers separated by commas or spaces. The calculator finds the mean and sample standard deviation, standardizes each value by subtracting the mean and dividing by that standard deviation, cubes each standardized value, sums the cubes, and scales the total by a small-sample correction factor based on n. The result is labeled symmetric, right-skewed, or left-skewed.

Skewness = [n / ((n-1)(n-2))] × Σ ((x_i - mean) / s)^3, where s is the sample standard deviation.

Formula & Methodology

By hand, first compute the mean and the sample standard deviation, dividing the sum of squared deviations by n-1, not n. For every value, subtract the mean, divide by the standard deviation, and cube the result. Add up all those cubes. Multiply that sum by n divided by the product of (n-1) and (n-2). A result near zero indicates rough symmetry; the sign of a larger result points to which tail is longer.

Examples

Right-Skewed Sample

For the values 2, 3, 3, 4, 4, 4, 5, 5, 9, the mean is 4.33 and the sample standard deviation is 2.0. Running those through the formula gives a skewness of approximately 1.70, labeled right-skewed because of the single high value of 9 pulling the tail outward.

Perfectly Symmetric Set

For the values 1, 2, 3, 4, 5, the deviations from the mean of 3 are evenly balanced on both sides, so the cubed standardized values cancel out exactly and skewness comes out to 0, labeled approximately symmetric.

Advantages

Puts a precise number on distribution shape instead of relying on eyeballing a histogram.
Distinguishes which direction a distribution leans, information that mean and standard deviation alone do not provide.
Uses a small-sample correction so it can be applied to modest datasets, not just very large ones.

Common Mistakes

Treating any nonzero skewness value as automatically meaningful, when small samples can produce noisy nonzero results even from data that is not truly skewed in the population it came from.
Misreading the sign: a positive value means the long tail stretches toward higher values, not that most values are high.
Comparing skewness figures computed from differently transformed versions of the same data, such as raw versus log-transformed, as if they described the same shape.

Edge Cases to Watch For

Requires at least 3 numbers, since the formula divides by (n-1)(n-2), which breaks down below that count.
If every value in the dataset is identical, the standard deviation is zero and skewness is mathematically undefined, so the calculator returns an error instead of a divide-by-zero result.
The shape label uses a fixed cutoff: absolute skewness under 0.5 is called approximately symmetric, above that it is labeled right-skewed or left-skewed based on sign; this is a descriptive heuristic, not a formal significance test.

Common Use Cases

Analysts checking whether a dataset like income or wait times looks close to symmetric before applying methods that assume it.
Quality engineers examining whether process measurements or defect counts cluster with a long tail of rare extreme cases.
Researchers describing distribution shape in a report with more precision than a mean and standard deviation alone provide.

Frequently asked questions

What does a positive vs negative skewness mean?

Positive skewness means the distribution has a longer tail stretching to the right (a few unusually high values), while negative skewness means a longer tail to the left (a few unusually low values). A skewness near zero suggests a roughly symmetric distribution.