How to Calculate the Pearson Correlation Coefficient (2026)

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from −1 to +1: a value near +1 means the variables rise together, near −1 means one rises as the other falls, and near 0 means no linear relationship. It is the most widely used correlation measure in statistics, research, and data analysis. Use the Pearson Correlation to compute r instantly from any pair of datasets.

The Formula and Manual Calculation

Pearson's r is calculated as the covariance of X and Y divided by the product of their standard deviations. In practice, the equivalent computational formula is easier to apply by hand: sum the products of paired values, subtract (ΣX × ΣY) / n, then divide by the square root of [ΣX² − (ΣX)²/n] × [ΣY² − (ΣY)²/n]. For a dataset with five pairs, work through four intermediate sums — ΣX, ΣY, ΣXY, ΣX², ΣY² — then plug them in. For anything beyond a handful of points, a calculator eliminates arithmetic errors that compound quickly.

Example: Hours Studied vs. Exam Score

The table below shows five students' study hours and exam scores. Computing r on this data yields approximately +0.98, indicating a very strong positive linear relationship.

Interpreting the Result

As a rule of thumb: |r| below 0.3 is weak, 0.3–0.7 is moderate, and above 0.7 is strong — though what counts as meaningful depends on the field. A high r only confirms a linear relationship; two variables can be strongly related in a curved way and still show r near 0. Correlation is also not causation — a high r between ice cream sales and drowning rates reflects a shared cause (hot weather), not a direct link. Always plot a scatterplot alongside r to spot non-linear patterns or outliers that can distort the coefficient. Use the Pearson Correlation to do this instantly.