Shapiro-Wilk Normality Test Calculator
Check whether your data are normal, with W and the p-value.
What the Shapiro-Wilk test does
The Shapiro-Wilk test checks whether a sample comes from a normal distribution. Many tests, such as the t-test, ANOVA and regression, assume normal data or normal residuals, so this is often the first check. The null hypothesis is that the data are normal. A small p-value (below 0.05) is evidence against normality, and a large one means you have no evidence against it.
Worked examples
- The default 40 exam scores: W = 0.9613, p = .185. There is no evidence against normality, so a t-test would be reasonable.
- A right-skewed sample (1.2, 2.3, 2.9, … 12.5, 20.1): W = 0.7623, p = .004. The data are not normal, so a rank-based test is safer.
How to read W
W is between 0 and 1 and compares the ordered values of your sample with the values you would expect from a perfect normal sample. A W close to 1 means the data look normal. The test works for 3 to 5,000 values, and the p-value uses Royston’s approximation.
Using the result well
- With small samples, the test has little power, so it can miss real departures from normality. With large samples, it flags tiny differences that do not matter. Always look at a histogram or a Q-Q plot too.
- For regression, test the residuals, not the raw data.
- If the data are not normal, you can transform them (for example with a logarithm) or use a non-parametric test such as the Mann-Whitney U test or the Kruskal-Wallis test.
To see the shape of your data, use the histogram maker.
How to cite this page
CalcPulse. (2026). Shapiro-Wilk Normality Test Calculator. https://calcpulse.com/shapiro-wilk-test-calculator/
Frequently asked questions
What is the Shapiro-Wilk test?
A statistical test of whether a sample comes from a normally distributed population.
What does a p-value below 0.05 mean?
The data are unlikely to be normal. A p-value above 0.05 means there is no evidence against normality.
How many values can I test?
From 3 to 5,000.
Should I rely on this test alone?
No. Also look at a histogram or Q-Q plot, because the test can miss non-normality in small samples and flag trivial differences in large ones.
What if my data are not normal?
Transform the data, or use a non-parametric test such as Mann-Whitney U, Wilcoxon signed-rank or Kruskal-Wallis.
Last updated