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Skewed Distribution Calculator | Skewness, kurtosis & shape

Measure how skewed your data is with sample skewness, excess kurtosis and the mean-versus-median comparison, with a plain-English shape classification. The fast way to understand distribution shape before choosing summary statistics.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Data setSkewness G₁Shape
2, 3, 5, 8, 14, 231.20Highly right-skewed
1, 2, 3, 4, 50Symmetric
23, 14, 8, 5, 3, 21.20Same values, same skew
10, 10, 9, 8, 5, 1−1.30Highly left-skewed

info Skewed Distribution Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

|Skewness|Interpretation
< 0.5Approximately symmetric
0.5 – 1.0Moderately skewed
> 1.0Highly skewed
SignPositive = right tail, negative = left tail

lightbulb Worked example

Let's say you are using the Skewed Distribution Calculator. Measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-English shape classification. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments

The Skewed Distribution Calculator is built on a well-established calculation method. It uses the formula G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments to turn your inputs into a reliable result. Measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-English shape classification. The steps are shown on the page so you can follow the reasoning from input to output.

  1. Paste at least three numbers, separated by commas, spaces or new lines.
  2. The tool computes the central moments of your data, then the adjusted Fisher–Pearson sample skewness G₁ (the same statistic Excel's SKEW and most stats packages report).
  3. Excess kurtosis G₂ is added for n ≥ 4 to flag heavy or light tails.
  4. Compare mean and median: a mean above the median is the classic signature of right skew.

Worked example: 2, 3, 5, 8, 14, 23 → skewness 1.2048 (highly right-skewed), excess kurtosis 0.727, mean 9.17 vs median 6.5.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I know if my distribution is skewed?
Enter the required values into the input fields and press the calculate button. The tool applies the formula G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments and returns the result with a short explanation of each step, so you can check the working yourself.
What is a right-skewed (positively skewed) distribution?
A distribution is right-skewed when most values cluster at the low end but a long tail extends toward high values, so the mean sits above the median. Examples include household income and house prices. The calculator measures this with the sample skewness formula G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5 and classifies the shape in plain English.
What is a left-skewed (negatively skewed) distribution?
The Skewed Distribution Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-English shape classification. There is no limit on usage, and it works on any device.
What does kurtosis add to skewness?
The Skewed Distribution Calculator is a free online tool that measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-english shape classification. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
Which skewness formula does this calculator use?
The Skewed Distribution Calculator uses the standard G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
What does the Skewed Distribution Calculator do?
Measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-English shape classification. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Skewed Distribution Calculator use?
The Skewed Distribution Calculator applies the standard formula: G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments. The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Skewed Distribution Calculator free and private?
Yes — the Skewed Distribution Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Skewed Distribution Calculator?
The Skewed Distribution Calculator applies the standard formula: G₁ = [√(n(n−1)) ÷ (n−2)] × m₃ ÷ m₂^1.5, where m₂ and m₃ are the 2nd and 3rd central moments. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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