Calculators
Skewness Calculator
Measure the asymmetry of a dataset with sample and population skewness privately in your browser.
Read the shape of a dataset with skewness.
Skewness measures how asymmetric a distribution is around its mean. The adjusted Fisher-Pearson sample skewness is G1 = n / ((n − 1)(n − 2)) × Σ((x − mean) ÷ s)³, using the sample standard deviation s; the population moment skewness is b1 = (1 ÷ n) × Σ((x − mean) ÷ σ)³, using the population standard deviation σ. For 1, 2, 3, 4, 10, the mean is 4, the sample skewness is about 1.70, and the distribution is right-skewed because the long tail runs toward larger values. A positive result is right-skewed, a negative result is left-skewed, and symmetric data such as 1, 2, 3, 4, 5 returns zero. As rough rules of thumb, an absolute sample skewness under 0.5 is approximately symmetric, between 0.5 and 1 is moderately skewed, and 1 or more is highly skewed; these bands are conventions, not tests. Skewness is undefined when every value is identical because there is no spread to compare against, so this calculator reports an error for that case. At least three values are required for the sample estimate. Enter 3 to 10000 finite signed numbers separated by commas, semicolons, spaces or newlines. Scientific notation is accepted; thousands separators are not. Use consistent units; skewness itself is unitless. Calculations scale deviations before summing cubes to reduce overflow, and results display up to 12 significant digits. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What does skewness measure?
Skewness measures the asymmetry of a dataset around its mean. A positive value means the long tail runs toward larger values; a negative value means the long tail runs toward smaller values. For 1, 2, 3, 4, 10, the sample skewness is about 1.70.
What is the difference between sample and population skewness?
Sample skewness G1 = n / ((n − 1)(n − 2)) × Σ((x − mean) / s)³ uses the sample standard deviation and is the common software estimate for observed data. Population skewness b1 = (1 / n) × Σ((x − mean) / σ)³ uses the population standard deviation. For 1, 2, 3, 4, 10 they are about 1.70 and 1.14.
How do I interpret the skewness value?
As rough rules of thumb, an absolute sample skewness under 0.5 is approximately symmetric, between 0.5 and 1 is moderately skewed, and 1 or more is highly skewed. Symmetric data such as 1, 2, 3, 4, 5 returns zero. These bands are conventions, not statistical tests.
Why does identical data return an error?
Skewness divides by the standard deviation, which is zero when every value is identical. With no spread there is no asymmetry to measure, so the calculator reports that skewness is undefined for that dataset.
What input and privacy limits apply?
Enter 3 to 10000 finite signed numbers separated by spaces, commas, semicolons or newlines. Do not use thousands separators; scientific notation is accepted. Calculations scale deviations before summing cubes, display up to 12 significant digits, and no data is uploaded.