Correlation Coefficient Calculator

Q: What if my relationship is curved?

Pearson r only measures linear association. Consider Spearman rank correlation for monotonic relationships or fit a nonlinear model.

Use this free Pearson correlation coefficient calculator to measure the strength and direction of the linear relationship between two variables. Enter five paired data points to get Pearson r, R-squared, and a step-by-step calculation breakdown.

Enter Values

First x value

First y value (paired with x1)

Second x value

Second y value

Third x value

Third y value

Fourth x value

Fourth y value

Fifth x value

Fifth y value

Result

Enter values above and click Calculate to see your result.

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Formula

r = sum((xi - x-bar)(yi - y-bar)) / sqrt(sum((xi - x-bar) squared) x sum((yi - y-bar) squared))

Compute the covariance of x and y and divide by the product of their individual standard deviations. This normalizes the covariance to a value between -1 and 1.

Worked Example

Data: (1,2), (2,4), (3,5), (4,4), (5,5) Step 1: x-bar = 3, y-bar = 4 Step 2: Deviation products: [4, 0, 0, 0, 2], sum = 6 Step 3: x squared deviations sum = 10, y squared deviations sum = 6 Step 4: r = 6 / sqrt(10 x 6) = 6 / 7.746 = 0.775 Step 5: R-squared = 0.600 Result: r = 0.775 (strong positive). 60% of y variance explained by x.

What Is the Pearson Correlation Coefficient?

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 to +1. It is the most widely used measure of association in statistics.

r = 1: perfect positive linear relationship
r = -1: perfect negative linear relationship
r = 0: no linear relationship (but nonlinear relationships may exist)
R-squared tells you the proportion of variance in y explained by x
Correlation does not imply causation
Pearson r only measures linear relationships. A perfect curve can have r = 0

Always plot your data first, as outliers and nonlinear patterns can make r misleading.

You can also calculate changes using our Correlation P-Value Calculator, Standard Deviation Calculator or T-Test Calculator.

Frequently Asked Questions

What does r close to 1 mean?

A strong positive linear relationship. As one variable increases, the other tends to increase proportionally.

Does correlation imply causation?

No. Two variables can be correlated due to a confounding variable, reverse causation, or coincidence. Ice cream sales and drowning deaths are correlated because both increase in summer.

What is R-squared?

R-squared is the square of r. It represents the proportion of variance in one variable explained by the other. R-squared = 0.64 means 64% of variation in y can be predicted from x.

What is a strong vs weak correlation?

General guide: |r| > 0.7 is strong, 0.4-0.7 is moderate, 0.2-0.4 is weak, < 0.2 is negligible. Context matters though.

What if my relationship is curved?

Pearson r only measures linear association. Consider Spearman rank correlation for monotonic relationships or fit a nonlinear model.

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