Skewness Calculator — Dataset Symmetry Measure
Paste a list of numbers to get the sample or population skewness — a measure of how asymmetrically the data is distributed around its mean — along with the median skewness, excess kurtosis, and key summary statistics.
Skewness type
Right-skewed (positive)
- 1
Mean x̄
Σxᵢ ÷ 10 = 7.1 - 2
Std deviation s
√(120.9 ÷ (10 − 1)) = 3.6652Square root of the variance; used to standardise each deviation. - 3
Σ((xᵢ − x̄) ÷ s)³
Σ ((xᵢ − 7.1) ÷ 3.6652)³ = 6.9609 - 4
Skewness G₁ (bias-corrected)
10 ÷ ((10 − 1) × (10 − 2)) × 6.9609 = 0.9668
How does this calculator work?
Skewness measures distribution asymmetry: 0 is symmetric, positive means right-skewed (long right tail), negative means left-skewed. The sample formula is G₁ = n/[(n−1)(n−2)] × Σ[(xᵢ−x̄)/s]³. Values outside ±0.5 suggest notable asymmetry; beyond ±1 is highly skewed.
Formula
How this is calculated
Skewness measures the asymmetry of a probability distribution or dataset. A skewness of 0 means the data is symmetric around its mean; positive values indicate a longer right tail (right-skewed or positively skewed); negative values indicate a longer left tail (left-skewed or negatively skewed). The Fisher-Pearson sample coefficient G₁ = n / [(n−1)(n−2)] × Σ[(xᵢ − x̄)/s]³ is the most widely used formula — it applies Bessel-style bias correction and is the default in software like Excel (SKEW function) and Python (pandas skew). The population (biased) formula g₁ simply divides by n without bias correction.
This calculator also reports Pearson's second skewness coefficient: 3 × (mean − median) / s. This non-parametric estimate is more robust to extreme outliers and is related to the empirical observation that for many real distributions, mean − mode ≈ 3 × (mean − median) (Pearson's mode skewness approximation). Excess kurtosis (Fisher definition) is returned as a bonus — a positive excess kurtosis means heavier tails than a normal distribution (leptokurtic).
At least 3 data points are required for the sample formula (which divides by (n−1)(n−2) — both factors must be positive). A dataset where all values are identical has zero standard deviation, making skewness undefined. As a rough guide: |G₁| < 0.5 is approximately symmetric; 0.5 ≤ |G₁| < 1 is moderately skewed; |G₁| ≥ 1 is highly skewed.
Frequently asked questions
A positive (right) skew means the right tail is longer — there are some unusually large values pulling the mean above the median. Income distributions and wait times are classic examples: most values cluster at the low end with a few very high values dragging the mean upward.
Excel's SKEW function computes the bias-corrected Fisher-Pearson sample skewness G₁ = n / [(n−1)(n−2)] × Σ[(xᵢ − x̄)/s]³ — the same formula this calculator uses for the "sample" option. Excel's SKEW.P function uses the population (biased) formula.
Perfectly normal data has a skewness of 0. In practice, values between −0.5 and +0.5 are generally treated as approximately symmetric. Values between ±0.5 and ±1 suggest moderate skew; beyond ±1 indicates high skew that can affect the validity of tests that assume normality.
Also known as
TG we-Calculate Editorial Team. (2026). Skewness Calculator — Dataset Symmetry Measure [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/skewness-calculator
TG we-Calculate Editorial Team. "Skewness Calculator — Dataset Symmetry Measure." TG we-Calculate. 2026. https://we-calculate.com/calculator/skewness-calculator.
TG we-Calculate Editorial Team, "Skewness Calculator — Dataset Symmetry Measure," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/skewness-calculator
@misc{wecalculate_skewness_calculator, title = {Skewness Calculator — Dataset Symmetry Measure}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/skewness-calculator}}, year = {2026}, note = {TG we-Calculate} }
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