Skewness Calculator

How to use this skewness and kurtosis calculator

What this calculator does

This calculator describes the shape of a numerical sample. It reports Excel-compatible adjusted Fisher – Pearson Skewness, which measures asymmetry, and Excess kurtosis, which compares tail weight and peakedness with a normal distribution on a scale where normal excess kurtosis is zero. It also computes the Mean, Sample standard deviation, Median, Minimum, Maximum, Range, and a row-by-row standardization table. These statistics are descriptive; they do not by themselves prove that data are normal or non-normal. For the underlying definitions, see the NIST guidance on measures of skewness and kurtosis.

When to use it

Use it when you want to compare the shape of small samples, check whether a business or scientific measurement has a long tail, inspect whether extreme values are pulling a distribution to one side, or reproduce spreadsheet skewness/kurtosis calculations outside a workbook. It is especially useful as an exploratory-data-analysis step before choosing a summary, transformation, or statistical model.

How to calculate

1. The calculator opens with an 18-value demonstration dataset and finite results. The matching example XLSX is immediately available through Download Excel.
2. Replace the values in Data (up to 30 numbers). Enter one number per line, or separate values with spaces or semicolons. Recalculation is live.
3. Read Skewness first for direction and magnitude, then Excess kurtosis for relative tail weight. Use the supporting location and spread statistics to understand scale.
4. Review the observation table when you need to see which values sit far from the mean. A large absolute Standardized deviation (z) shows an observation many sample standard deviations from the mean.
5. Select Download Excel to export the current validated inputs and canonical results as a real OOXML workbook. Reset clears the demonstration/input data and results; after Reset, Excel export remains disabled until a complete valid dataset is entered again.

Input guide

Data (up to 30 numbers) is the only semantic input and is required. Enter 3 – 30 finite real numbers, with absolute values no greater than 1×10¹⁰⁰. The accepted decimal convention uses a period, so 1.5 is valid while 1,5 is rejected rather than silently reinterpreted. Scientific notation such as 1e3 is accepted. Skewness requires at least three observations; excess kurtosis requires at least four. All observations must not be identical because a zero sample standard deviation makes standardized moments undefined. Adding or changing an extreme value can strongly change skewness and kurtosis, so confirm that pasted values and units are consistent.

Output guide

Count is the exact number of observations. Mean is the arithmetic average; Median is the middle location statistic. Minimum, Maximum, and Range describe the observed span. Sample standard deviation uses the n – 1 denominator and measures spread in the same unit as the input. Skewness and Excess kurtosis are dimensionless. A skewness near zero indicates relative symmetry; positive values indicate a longer right tail and negative values a longer left tail. The live Shape pill compresses the same sign-and-magnitude interpretation into a short summary. The displayed Skewness reading uses common descriptive bands: |skewness| ≤ 0.5 approximately symmetric, 0.5 – 1 moderately skewed, and above 1 substantially skewed. The Kurtosis reading describes the sign and flags magnitudes above 1 or below – 1 as substantial. The table columns Index, Value, Deviation from mean, and Standardized deviation (z) show entered order, raw data, distance from the mean, and that distance divided by the sample standard deviation. These are exact calculations from the current sample, subject only to display rounding.

Worked example

The opening sample contains 18 values from 140 to 172. Their mean is 157.5000 and their sample standard deviation is 8.8334. Applying the adjusted sample formulas produces Skewness = – 0.3212 and Excess kurtosis = – 0.7195. The skewness is close to zero with a mild left-tail tendency, while the negative excess kurtosis indicates a lighter-tailed/flatter sample than a normal distribution. These first-open values match the result cards and the downloadable workbook. Microsoft documents the same sample skewness convention in its Excel SKEW function reference.