CalcaTools

Skewed Distribution Calculator

Measures how skewed a data set is: sample skewness, excess kurtosis, mean vs median and a plain-English shape classification.

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

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

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

Formula & methodology

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

  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.

Frequently asked questions

How do I know if my distribution is skewed?
Compute the sample skewness: values beyond ±0.5 indicate noticeable asymmetry and beyond ±1 strong asymmetry. A quick visual check is mean ≠ median — the mean gets pulled toward the long tail.
What is a right-skewed (positively skewed) distribution?
One with a long tail of high values: most observations sit low but a few large ones stretch the right side. Income, house prices and insurance claims are classic examples; mean > median.
What is a left-skewed (negatively skewed) distribution?
The mirror image: a long tail of low values, with mean < median. Exam scores on an easy test and age at death in developed countries are typically left-skewed.
What does kurtosis add to skewness?
Skewness measures asymmetry; excess kurtosis measures tail weight. Positive excess kurtosis means more outliers than a normal distribution, negative means fewer. A normal distribution scores 0 on both.
Which skewness formula does this calculator use?
The adjusted Fisher–Pearson standardized moment coefficient G₁ = √(n(n−1))/(n−2) × g₁ — the same one Excel's SKEW function, R's e1071 (type 2) and SPSS report.

Explore the full statistics toolkit

Every CalcaTools statistics calculator — descriptive measures, probability distributions, hypothesis tests, confidence intervals, and Six Sigma process metrics — with step-by-step workings on each result.

Process quality