r Critical Value Table for Pearson Correlation

July 11, 2026 4 min read Joseph Mburu

Statistical Tables

Use this interactive correlation critical value table to find the critical value for Pearson’s correlation coefficient. Select the tail type (two-tailed, right-tailed, or left-tailed), choose the significance level, enter the degrees of freedom, and the correct critical value will be highlighted.

Tail Type

Two-tailed

Right-tailed

Left-tailed

Two-tailed is the default for most correlation tests. Use a one-tailed table only when the alternative hypothesis specifies a positive or negative direction.

Significance Level, α

The default is α = 0.05.

Degrees of Freedom, df

For Pearson correlation, df = n − 2.

Two-Tailed Pearson Correlation r Critical Value Table

Values are critical values of Pearson’s r. Enter df and select α to highlight the matching table value.

Note: Correlation tests are usually two-tailed by default because we often test whether r is different from 0 in either direction. Use a right-tailed or left-tailed table only when the problem specifically asks you to test a direction, such as a positive or negative correlation.

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