Skewness Calculator
Measure the asymmetry of your data in seconds. This free skewness calculator finds the adjusted Fisher-Pearson coefficient (the same value Excel and SPSS return), tells you whether your distribution is skewed left or right, and shows every step alongside a live histogram.
Textbook-accurate · Reviewed July 2026 · Primary result matches Excel’s SKEW function (adjusted Fisher-Pearson)
Enter Your Data
Works with commas, spaces, tabs, or line breaks. Decimals and negatives are fine. You need at least 3 values.
The calculator reports the adjusted Fisher-Pearson coefficient (G₁) as its headline result — the version used by Excel, SPSS, and SAS — and also shows the moment coefficient and both Pearson coefficients for comparison.
Your Result
Distribution Shape
Histogram with mean and median marked
- Frequency
- Mean
- Median
What Is Skewness?
Skewness is a measure of the asymmetry of a distribution — how lopsided your data is. In a perfectly symmetrical distribution like the normal bell curve, the left and right sides mirror each other and the skewness is zero. But real-world data rarely behaves so neatly. When values pile up on one side and trail off in a longer tail on the other, the distribution is skewed, and the skewness coefficient tells you both the direction of that lean and how pronounced it is.
The sign is the first thing to read. A positive skewness value means the longer tail points to the right (toward larger values); a negative value means the longer tail points to the left (toward smaller values); and a value near zero means the data is roughly symmetric. That single number captures something a mean and standard deviation alone can’t: the shape of your data.
Positive vs. Negative Skew: How to Tell the Difference
The two directions of skew are the most-searched aspect of the topic, and the distinction is simple once you picture the tail.
Positive skew (right-skewed)
In a positively skewed (or right-skewed) distribution, most values cluster at the lower end and a few large values stretch a long tail to the right. The classic example is income: most people earn modest amounts while a small number of very high earners pull the tail rightward. Because those large values drag the average up, the mean is greater than the median in a right-skewed distribution. Response times, house prices, and city populations are all typically right-skewed.
Negative skew (left-skewed)
In a negatively skewed (or left-skewed) distribution, most values cluster at the higher end and a few small values stretch a long tail to the left. Scores on an easy exam are a good example: most students score high, with a handful of low scores forming the left tail. Here the mean is less than the median. Age at death in a developed country and the number of fingers people have are other everyday examples of left skew.
| Positive (right) skew | Negative (left) skew | |
|---|---|---|
| Longer tail points | Right (toward high values) | Left (toward low values) |
| Skewness value | Greater than 0 | Less than 0 |
| Mean vs. median | Mean > median | Mean < median |
| Typical order | Mode < median < mean | Mean < median < mode |
| Real-world example | Income, house prices | Easy exam scores, age at death |
How to Calculate Skewness
The most widely used measure — and the one this calculator reports as its headline result — is the adjusted Fisher-Pearson standardized moment coefficient, written G₁. It’s the value Excel’s SKEW function, SPSS, and SAS all return:
G₁ = [ n / ((n − 1)(n − 2)) ] × Σ ((xᵢ − x̄) / s)³
where n is the number of values, x̄ is the mean, and s is the sample standard deviation. In plain terms: you standardize each value (subtract the mean, divide by the standard deviation), cube it, add them all up, and apply a correction factor that adjusts for sample size. Cubing is the crucial step — it preserves the sign of each deviation, so values far out in one tail dominate and reveal the direction of the lean.
Pearson’s coefficients of skewness
There are two simpler alternatives developed by Karl Pearson, useful when you already know the mean, median, mode, and standard deviation. This calculator computes both for comparison:
- Pearson’s first coefficient (mode): (mean − mode) / standard deviation
- Pearson’s second coefficient (median): 3 × (mean − median) / standard deviation
The second coefficient is the more commonly used of the two, since the mode can be unreliable in small or continuous datasets. All these measures share the same sign convention: positive means right-skewed, negative means left-skewed.
How to Interpret a Skewness Value
Once you have a skewness number, the sign tells you the direction and the magnitude tells you the strength. There’s no single official cutoff, but statisticians widely use these rules of thumb:
| Skewness value | Interpretation |
|---|---|
| Between −0.5 and +0.5 | Approximately symmetric |
| −1 to −0.5, or +0.5 to +1 | Moderately skewed |
| Less than −1, or greater than +1 | Highly skewed |
These bands are guidelines, not laws — the right threshold depends on your field and sample size. As a practical matter, the further the value sits from zero, the more asymmetric your data, and the more you should think twice before applying methods that assume a symmetric (normal) distribution. The calculator applies exactly these bands to label your result automatically.
Skewness, the Mean, and the Median
One of the most useful practical consequences of skewness is what it does to your averages. In a symmetric distribution, the mean and median are roughly equal. But skew pulls the mean toward the long tail, because the mean is sensitive to extreme values while the median is not. That’s why, for right-skewed data like income, the median is usually reported instead of the mean — the median better represents the “typical” value when a few extreme observations would otherwise distort the picture. You can compute both for your data with our Descriptive Statistics Calculator, which reports the mean, median, and skewness side by side.
Why Skewness Matters
- Finance: the skewness of investment returns signals tail risk. Negative skew warns of occasional large losses; positive skew suggests occasional large gains.
- Choosing the right average: skew tells you whether the mean or the median better summarizes your data.
- Statistical assumptions: many tests assume normality; strong skew is a red flag that a transformation or a non-parametric method may be needed.
- Quality control & research: skew can reveal hidden processes, measurement floors or ceilings, or the influence of outliers.
- Test design: in psychometrics, skew exposes ceiling and floor effects — a test that’s too easy or too hard for its takers.
Skewness describes the tails’ direction; its companion measure, kurtosis, describes the tails’ weight. The two are almost always analyzed together to fully characterize a distribution’s shape.
Frequently Asked Questions
Skewness measures how asymmetric or lopsided a distribution is. If you draw a histogram of your data, skewness tells you which side has the longer tail. A positive skewness means the tail stretches to the right toward larger values; a negative skewness means it stretches to the left toward smaller values; and a value near zero means the data is roughly symmetric, like a normal bell curve. It captures the shape of your data, not just its center or spread.
Positive skew (right-skewed) means the longer tail is on the right: most values are small, but a few large values stretch the distribution rightward, and the mean ends up greater than the median. Income is a classic example. Negative skew (left-skewed) means the longer tail is on the left: most values are large, with a few small ones pulling the tail left, and the mean is less than the median. Scores on an easy test are a common example.
Read the sign first, then the size. A positive value means right-skewed and a negative value means left-skewed. For magnitude, a common rule of thumb is: between −0.5 and +0.5 is approximately symmetric, between 0.5 and 1 (either sign) is moderately skewed, and beyond ±1 is highly skewed. These are guidelines rather than strict rules, and the appropriate thresholds can vary with your field and sample size.
A skewness of exactly zero indicates perfect symmetry, as in a normal distribution. In practice, values between −0.5 and +0.5 are usually treated as approximately symmetric and acceptable for methods that assume normality. Many analysts consider skewness within ±1 tolerable, while values beyond ±1 signal substantial asymmetry that may warrant a data transformation or a non-parametric approach. The acceptable range ultimately depends on the specific analysis and how sensitive it is to non-normality.
Excel’s SKEW function uses the adjusted Fisher-Pearson standardized moment coefficient, often written G₁, which corrects for sample size. This is the same measure reported by SPSS and SAS and is the headline result in this calculator. Excel also has a SKEW.P function that uses the population version without the sample-size correction. If your result differs from another tool, check whether it’s using the sample-adjusted or population version.
Yes. A negative skewness value is completely normal and simply means the distribution is left-skewed — its longer tail points toward smaller values, and the mean sits below the median. There’s nothing wrong with negative skew; it’s just one of the two possible directions of asymmetry. Examples include scores on an easy exam and age at death in countries with long life expectancy, where most values are high and a few low ones form the left tail.
Methodology & formulas used
This calculator computes multiple skewness measures, reviewed July 2026. All computation runs locally in your browser; your data is never uploaded.
- Adjusted Fisher-Pearson G₁ (headline, matches Excel SKEW): [n / ((n − 1)(n − 2))] × Σ((xᵢ − x̄)/s)³, where s is the sample standard deviation. Requires at least 3 values.
- Moment coefficient g₁: m₃ / m₂^(3/2), using the population moments m₂ and m₃ about the mean — the “biased” version.
- Pearson’s first coefficient (mode): (mean − mode) / s. Shown only when a single clear mode exists.
- Pearson’s second coefficient (median): 3 × (mean − median) / s.
- Interpretation bands: |skew| < 0.5 approximately symmetric; 0.5–1 moderately skewed; > 1 highly skewed.
The sample standard deviation used here divides by n − 1. Different tools use slightly different conventions (sample vs. population), so results can vary. Results are rounded for display but computed at full precision.
References
- Joanes, D.N. & Gill, C.A. (1998). Comparing measures of sample skewness and kurtosis. Skewness overview
- NIST/SEMATECH e-Handbook of Statistical Methods. Measures of Skewness and Kurtosis. itl.nist.gov
- Wikipedia. Skewness — definitions, formulas, and examples. en.wikipedia.org