About the Skewness and Kurtosis Calculator
Mean and standard deviation do not tell the whole story of a data set. Skewness tells you whether the values are lopsided, with a long tail on the right or on the left. Kurtosis tells you how heavy the tails are compared with a bell curve. Paste your numbers and this calculator gives both, in the sample form used by most software and in the population form, and describes the shape in words. Type your numbers and the skewness and kurtosis appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Skewness and Kurtosis Calculator
- 1Enter your numbers.
- 2Pick the units or options from the menus if the skewness and kurtosis tool offers them.
- 3Read the skewness and kurtosis in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the skewness and kurtosis
Analysts use skewness to decide whether to use the mean or the median, or whether to transform the data with a logarithm. Kurtosis flags data with extreme values, which matters in finance, quality control and tests that assume a normal shape.
A symmetric data set has skewness near 0. As a rough guide, values between −0.5 and 0.5 are fairly symmetric, and beyond 1 or −1 are strongly skewed. Excess kurtosis of 0 matches a normal distribution; positive means heavier tails, negative lighter.
How the skewness and kurtosis is worked out
Skewness g1 = m3 ÷ m2^1.5, where m2 and m3 are the second and third central moments. The sample version multiplies by √(n(n − 1)) ÷ (n − 2). Excess kurtosis is m4 ÷ m2² − 3, with a sample correction for n of 4 or more. The numbers 2, 4, 4, 4, 5, 5, 7, 9, 12 have a mean of 5.78. The sample skewness is 1.13, so the data are skewed to the right, with the 12 pulling the tail. The sample excess kurtosis is 0.96, a little heavier-tailed than a normal curve.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Sample and population values
- Shape described in words
- Any list of numbers
Mistakes to avoid with skewness and kurtosis
Small samples give unreliable skewness and kurtosis, so do not read too much into a few numbers. The sample skewness needs at least three values and the sample kurtosis at least four. If all values are equal the shape is not defined.
On phone and computer
On a phone, type into the boxes one after another and read the skewness and kurtosis underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the skewness and kurtosis move. The skewness and kurtosis calculator works the same on both. Shape measures are best read with the centre and spread. Find the spread with the Standard Deviation Calculator, the squared spread with the Variance Calculator, and unusual values with the Outlier Calculator.
Features
- Needs at least 3 numbers
- Small samples are noisy
- Compare with the median
- Clear messages when the skewness and kurtosis inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate skewness and kurtosis?
Skewness g1 = m3 ÷ m2^1.5, where m2 and m3 are the second and third central moments. The sample version multiplies by √(n(n − 1)) ÷ (n − 2). Excess kurtosis is m4 ÷ m2² − 3, with a sample correction for n of 4 or more. The numbers 2, 4, 4, 4, 5, 5, 7, 9, 12 have a mean of 5.78. The sample skewness is 1.13, so the data are skewed to the right, with the 12 pulling the tail. The sample excess kurtosis is 0.96, a little heavier-tailed than a normal curve.
What is the formula for skewness and kurtosis?
Skewness g1 = m3 ÷ m2^1.5, where m2 and m3 are the second and third central moments. The sample version multiplies by √(n(n − 1)) ÷ (n − 2). Excess kurtosis is m4 ÷ m2² − 3, with a sample correction for n of 4 or more. The skewness and kurtosis calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is positive skew?
A long tail to the right, with a few unusually large values. The mean is then above the median.
What does excess kurtosis mean?
Kurtosis minus 3, so that a normal distribution scores 0. Positive means more extreme values than normal.
Which version should I use?
The sample versions for data that are a sample from a bigger group, which is the usual case.
Is this skewness and kurtosis calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.