Pearson Correlation Calculator – Find r and r² in 2 Easy Steps

Use this free Pearson correlation calculator to measure the strength and direction of the straight-line relationship between two variables.

Pearson’s r is the most widely used correlation statistic. Researchers, students and analysts use it to check whether advertising spend tracks sales, whether study time tracks grades, or whether two sensors agree.

Working it out by hand means finding means, deviations, products and square roots for every pair. Our Pearson correlation calculator does it instantly and adds r² and a plain-English label so the result is easy to report.

Pearson Correlation Formula

r = Σ(xᵢ − x̄)(yᵢ − ȳ) / √[ Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)² ]

x̄, ȳ = means of X and Y
r²    = share of variation in Y explained by a straight line on X

The numerator measures how X and Y vary together (covariance). The denominator scales it by the spread of each variable, so r always falls between −1 and +1 and does not depend on units.

Worked Examples

Example 1: study hours and exam scores

X = 1, 2, 3, 4, 5, 6, 7, 8 hours and Y = 52, 55, 61, 64, 70, 72, 79, 83 marks. The calculator gives r = 0.9962 and r² = 0.9924, so about 99% of the variation in scores lines up with study time in this sample.

Example 2: price and units sold

Prices of 10, 20, 30, 40 and 50 with sales of 90, 75, 70, 55 and 40 units give r = −0.9897. The negative sign shows that higher prices go with fewer sales.

Example 3: a weak relationship

Heights 60, 62, 65, 68, 70, 72 and test scores 55, 70, 58, 72, 60, 66 give r = 0.3029, a weak positive relationship that could easily be chance with only six pairs.

How to Use the Pearson Correlation Calculator

Step 1: Enter the X and Y Data

Paste the first variable into Variable X (Independent) and the second into Variable Y (Dependent), separated by commas or new lines. Each X value must line up with its Y value, and both lists must be the same length. Click Calculate Correlation.

Step 2: Read r, r² and the Strength Label

The Correlation Analysis Report shows Pearson r, R-squared (r²), the sample size N and a label such as “Very Strong Positive Correlation”. Use Share or Download to keep the result.

How to Interpret Pearson r

These bands are a widely used rule of thumb. What counts as strong depends on the field: r = 0.3 can matter in social science, while lab measurements often need r above 0.95.

Assumptions to Check

• Linear pattern: plot the data first. A curved pattern can give a low r even when the variables are clearly related.
• Numeric data: both variables should be measured on an interval or ratio scale.
• No extreme outliers: one unusual point can raise or lower r a lot.
• Paired observations: each X must belong to the same case as its Y.

If your data are ranks, are skewed, or have outliers, use Spearman’s rank correlation instead.

Correlation Is Not Causation

A strong r tells you two variables move together, not that one causes the other. Ice cream sales and sunburn cases are strongly correlated because both rise in hot weather. Use experiments or regression with control variables to study cause and effect.

Common Mistakes

• Entering X and Y in different orders so pairs no longer match.
• Treating r² as a percentage of cases rather than of variation.
• Calling a correlation significant without a significance test or enough data.
• Using r for a clearly curved relationship.

Frequently Asked Questions