Normality Test Calculator

Use this Normality Test Calculator to determine whether a dataset is consistent with a normal distribution. Paste or type your numbers into the single input box—values can be separated by commas, spaces, or line breaks. Copy and pasting from a spreadsheet column is acceptable. Text is ignored. Click Analyze to compute core sample statistics (mean, median, standard deviation, range, skewness, and excess kurtosis), and to generate a results printout you can save or share.

The normality test calculator runs three standard goodness-of-fit tests and reports their test statistics and p-values: Shapiro-Wilk (W), Kolmogorov-Smirnov (D; Lilliefors p-value when μ and σ are estimated), and Anderson-Darling (A²; Stephens-adjusted p-value). It also draws a Q-Q plot and a histogram with an overlaid normal curve for visual assessment. Smaller p-values indicate stronger evidence against normality. Additional guidance and notes are below the calculator. See all my Statistical Calculators!

Interpreting the Normality Test Calculator Results

This Normality Test Calculator performs three goodness-of-fit tests that determines whether your sample data were drawn from a population that follows a normal distribution. These tests are hypothesis tests and, like any statistical hypothesis test, they have a null hypothesis and an alternative hypothesis.

• H₀: The sample data follow the normal distribution.
• H₁: The sample data do not follow the normal distribution.

In the Normality Test Calculator results, small p-values indicate that you can reject the null hypothesis and conclude that your data were not drawn from a population that follows a distribution. Consequently, distribution tests are a rare case where you look for high p-values to identify candidate distributions. Learn more about Goodness of Fit: Definition & Tests.

This Normality Test Calculator includes three different methods for statistically evaluating your data, which I compare and contrast below. However, you should always use these tests in tandem with a visual assessment in a Q-Q plot.

Learn more in-depth about the Normal Distribution.

Visual Assessment

Q-Q plots might be the best way to determine whether your data follow a particular distribution. Consequently, I’ve included a Q-Q plot in this normality test calculator. If your data follow the straight line on the graph, the distribution fits your data. This process is simple to do visually. Informally, this process is called the “fat pencil” test. If all the data points line up within the area of a fat pencil laid over the center straight line, you can conclude that your data follow the distribution.

Q-Q plots are especially useful in cases where the distribution tests are too powerful. Distribution tests are like other hypothesis tests. As the sample size increases, the statistical power of the test also increases. With very large sample sizes, the test can have so much power that trivial departures from the distribution produce statistically significant results. In these cases, your p-value will be less than the significance level even when your data follow the distribution.

The solution is to assess Q-Q plots to identify the distribution of your data. If the data points fall along the straight line, you can conclude the data follow that distribution even if the p-value is statistically significant. Learn more about QQ Plots: Uses, Benefits & Interpreting.

Comparing the Normality Tests

This normality test calculator provides three standard distribution tests. Below is a discussion of their methods and relative strengths and weaknesses.

When all three tests point the same way, you’re in good shape—treat the conclusion as robust. If they diverge, it’s usually because each test weighs different features of the data (center vs. tails, correlation vs. CDF). The discussion below explains how each method works, its strengths and caveats, and how to decide which result to trust.

Shapiro-Wilk (W)

The Shapiro-Wilk test assesses whether your ordered data look like ordered normal quantiles–akin to how a Q-Q plot works. To answer this question, the Shapiro-Wilk test builds a weighted correlation-style statistic. Big departures from the diagonal straight line lower W and produce small p-values. In practice it’s the most powerful choice for small to moderate samples in a normality test calculator, catching both skew and heavy tails efficiently.

• Pros: excellent power with n ≈ 8–200, good all-around sensitivity, and it aligns closely with what you see in the Q-Q plot.
• Cons: with very large samples, even trivial deviations trigger significance; with heavily rounded data (many ties) performance degrades.

Use Shapiro-Wilk for continuous data without extreme rounding, especially when sample size is modest. Be cautious interpreting tiny p-values when n is in the thousands and always pair it with the Q-Q plot.

Kolmogorov-Smirnov (D; Lilliefors p-value)

The Kolmogorov-Smirnov test compares your empirical CDF to a fitted normal CDF and takes the maximum vertical gap as D. It’s easy to interpret and broadly applicable, which is why many normality test calculators include it.

• Pros: simple, parameter-free shape check once you account for estimating μ and σ (the Lilliefors p-value our calculator reports), and it’s less swayed by a few outliers than A-D.
• Cons: it’s least sensitive in the tails (where normality often fails) and loses power relative to Shapiro-Wilk for many alternatives; it also doesn’t love data with many ties or discrete steps.

Use KS when you want a conservative, center-focused check or a second opinion alongside Shapiro-Wilk. Avoid leaning on KS alone when tail fit matters (reliability, risk, SPC limits) or when data are coarsely rounded.

Anderson-Darling (A²; Stephens-adjusted p-value)

The Anderson-Darling test is another CDF-based test, but it weights the tails more heavily, so mismatches out where the normal curve thins count extra. That makes it a great complement in a normality test calculator when you care about extremes.

• Pros: excellent tail sensitivity and good overall power; the Stephens adjustment (used here) gives appropriate p-values when μ and σ are estimated.
• Cons: it can “over-react” to a single outlier or slight tail curvature in very large samples, and—like KS—ties and discrete measurements can blunt the test.

Use A-D when tail behavior is important (reliability, tolerance intervals, process capability), and interpret results together with the Q-Q plot. Avoid treating a tiny p-value as decisive if a single data point is an obvious one-off or if measurements are strongly rounded.