Chi-Square Table (Chi-Square Distribution Table)

What Is a Chi-Square Table?

A chi-square table, also known as the chi-square distribution table or chi-square critical value table, is a reference table used to find critical values from the chi-square distribution. You may need this table to find χ² critical values whenever you’re working with tests such as:

• chi-square goodness-of-fit test
• chi-square test of independence
• chi-square test for a single population variance
• confidence intervals for a population variance or standard deviation

How to Use This Chi-Square Table

This interactive chi-square table allows you to automatically find the correct right-tailed critical value, without manual lookup. To use the table:

1. Select the Right-Tail Probability, α
2. Select the degrees of freedom, df
3. Click “Find Critical Values”.

The table will instantly highlight the correct critical value for your selected significance level (α) and degrees of freedom (df).

Note. This table includes the following right-tail probabilities:

• 0.995
• 0.99
• 0.975
• 0.95
• 0.90
• 0.10
• 0.05
• 0.025
• 0.01
• 0.005

Download the Chi-Square Table as a PDF

Want to find the chi-square critical values offline? You can also save the table in PDF format. You only need to click the print/save as PDF button and save it on your machine. The PDF format is helpful when you want to:

• use the table during revision
• include it in class notes
• print a copy for exam practice
• keep a quick reference for homework or data analysis

The PDF version keeps the same df rows and probability columns shown in the online table.

How to Read a Chi-Square Table

The chi-square table has the right-tail probability (or significance level, α) as the columns and degrees of freedom (df) as the rows. Therefore, to find the critical value using the table, follow these steps:

1. Find the specific column matching your significance level (α)
2. Move down the leftmost column to locate the degrees of freedom (df)
3. The value where α and df meet is the chi-square critical value

Example

A researcher is investigating whether a standard 6-sided die is fair. They roll the die 60 times and record the frequencies of each face. To determine if the observed frequencies significantly deviate from the expected uniform distribution, they decide to perform a Chi-Square goodness-of-fit test at a 5% significance level (α = 0.05). Based on this scenario, what is the correct critical value of Chi-Square for this test?

Solution

From the question, this is a chi-square goodness-of-fit test problem. By definition, the degrees of freedom for the chi-square goodness-of-fit test is: df = k-1, where k is the number of categories.

Since the die is 6-sided, we’ll have 6 categories. Therefore, df = 6-1

= 5.

Now, we know that:

• df = 5
• α = 0.05

To find the critical value from the chi-square table:

1. Find the specific column matching α = 0.05
2. Move down the leftmost column to locate df = 5
3. The value where α and df meet is 11.070

Therefore, the critical value for the test is: χ²_0.05, 5 = 11.070, as shown below.

Can’t see the exact degrees of freedom in the table? Use the chi-square critical value calculator to get precise results.

Degrees of Freedom for Chi-Square Tests

The degrees of freedom depend on the test you are running. For a chi-square goodness-of-fit test: df = k – 1, where k is the number of categories. However, for a chi-square test of independence: df = (r – 1)(c – 1), where r is the number of rows and c is the number of columns.

Want to learn how to calculate degrees of freedom for chi-square tests? Use the degrees of freedom calculator.

Frequently Asked Questions