r Critical Value Table for Pearson Correlation

By StatCalc.net Team Reviewed by Joseph Mburu, MSc — Senior Statistician & Editor Last updated October 19, 2026 4 min read

Use this Pearson correlation critical value table to find critical r values for two-tailed, right-tailed, and left-tailed tests at α = 0.10, 0.05, 0.02, 0.01, and 0.001. Hover over a value to trace its significance level and degrees of freedom, or click the value to view the corresponding critical region for Pearson's r.

Two-Tailed Pearson Correlation Critical Value Table

Critical values for testing whether Pearson's r differs from zero in either direction.

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Note: For Pearson correlation, df = n − 2. A two-tailed test has critical values at both −r and +r. A right-tailed test uses a positive critical value, while a left-tailed test uses the corresponding negative critical value.

What Is an r Critical Value Table?

An r critical value table, also known as a correlation critical value table, is a statistical table that provides cutoff values used to determine whether a Pearson correlation coefficient is statistically significant. We com

In this case, we compare the calculated Pearson’s correlation coefficient (r) with the r-critical value from the table and make decisions as follows:

Reject the null hypothesis (H₀) if the absolute value of the correlation coefficient |r| is greater than or equal to the absolute r-critical value. This implies that the linear relationship is statistically significant.
Fail to reject the null hypothesis (H₀) if the absolute value of the correlation coefficient |r| is less than the r-critical value. This implies that the linear relationship is not statistically significant.

How to Use This Interactive Correlation Critical Value Table

This interactive correlation critical value table makes it easy for you to look up the correct critical value within a few clicks. To use the table:

Select whether you are conducting a one-tailed or two-tailed test. Most correlation tests are two-tailed unless otherwise stated.
Select the significance level from the dropdown and enter the correct degrees of freedom (df)
Click the “Find Critical Value” button

The table will instantly highlight the correct r critical value for your test.

Recall. Use a one-tailed test when your hypothesis predicts a specific direction of the linear relationship.

How to Read the r Critical Value Table

The r-critical value table lists df on the rows and significance level (α) on the columns. Therefore, to read the correct correlation critical value for your test:

Identify the tail of the test. Most correlation tests are two-tailed unless otherwise stated.
Identify the significance level (α)
Compute the degrees of freedom (df)
Find the value where the α column meets the df row. This is the r critical value.

Example

Suppose you have a sample of 20 paired observations and are conducting a two-tailed test at α = 0.05 to determine whether the number of hours spent studying is correlated with the final exam score. Find the r critical value using tables.

Solution

To find the correlation critical value using the table, follow these steps:

Step 1. Identify the test type

Since the aim is to determine whether the linear relationship is statistically significant regardless of the direction, this is a two-tailed test. Therefore, we should use a two-tailed r-critical value table.

Step 2. Identify the significance level

From the question, α = 0.05

Step 3. Compute the degrees of freedom

By definition, the degrees of freedom formula for Pearson’s correlation test is: df = n-2, where n is the number of paired observations.

Since there are 20 pairs, df = 20-2

= 18

Want a quick way to calculate the correct degrees of freedom for your Pearson’s correlation test? Use the degrees of freedom calculator.

Step 4. Find the value where the α column meets the row.

The α = 0.05 column meets the df=18 row at 0.4438. Therefore, the r critical value for the test is ±0.4438.

Finding critical value using r-critical value table example

Want a quick way to find the correlation critical value without using tables? Use the r critical value calculator instead.

Frequently Asked Questions

What is an r critical value table?

An r critical value table lists the minimum Pearson correlation coefficient required for statistical significance at a given significance level and number of degrees of freedom. You compare your calculated correlation coefficient with the table value to determine whether the correlation is statistically significant.

How do I find the critical value of r using the table?

First, calculate the degrees of freedom using df = n − 2, where n is the number of paired observations. Next, choose the significance level and whether the test is one-tailed or two-tailed. The value at the intersection of the selected degrees of freedom and significance level is the critical value of r.

Should I use a one-tailed or two-tailed table?

Use a two-tailed table when testing whether a correlation exists in either direction (this is the most common choice). However, if the alternative hypothesis specifies a direction before the data are analyzed, such as testing specifically for a positive or negative correlation, use a one-tailed table (left- or right-tailed).

Can this table be used for Spearman correlation?

This table is designed for Pearson’s correlation coefficient and should not normally be used as an exact critical value table for Spearman’s rank correlation. Spearman correlation has its own critical values, especially for small samples