Correlation Coefficient Calculator
Enter two equal-length lists of numbers to compute the Pearson correlation coefficient between them.
Strong positive correlation
Formula
How this is calculated
You supply two equal-length lists, X and Y, where each Xᵢ is paired with the Yᵢ in the same position (the order matters, since the calculator only compares values at matching positions). It first finds the mean of each list, x̄ and ȳ, then for every pair measures the deviations dx = xᵢ − x̄ and dy = yᵢ − ȳ.
The numerator sums the products dx·dy (the covariance term): it is positive when X and Y tend to be above or below their means together, and negative when one is high while the other is low. The denominator, √(Σdx² × Σdy²), rescales that sum by each list's spread, so r is dimensionless and always falls between −1 and +1 regardless of the original units. r² is simply r squared — the share of variance shared linearly — and the regression slope is Σdx·dy ÷ Σdx².
Pearson's r only detects straight-line patterns, assumes the pairs are independent, and is sensitive to outliers. It needs at least two pairs and breaks down (undefined) if either list has zero variation. A correlation never proves that one variable causes the other.
About this calculator
The Pearson correlation coefficient, r, measures how strongly two variables move together in a straight-line relationship. It ranges from −1 to +1: a value near +1 indicates a strong positive relationship (as one variable rises, so does the other), a value near −1 indicates a strong negative relationship, and a value near 0 indicates little or no linear relationship.
Provide two lists of equal length, where each X is paired with the Y on the same position. The calculator also reports r², the coefficient of determination, which is the proportion of variance in one variable explained by the other, along with the slope of the best-fit regression line. Remember that correlation does not imply causation, and Pearson’s r only captures linear relationships — two variables can be strongly related in a curved pattern yet have an r close to zero.
Frequently asked questions
It measures the strength and direction of the linear relationship between two variables. Values near +1 or −1 indicate strong relationships, while values near 0 indicate weak or no linear relationship.
No. Correlation does not imply causation. Two variables can be strongly correlated because of coincidence or a third underlying factor, not because one causes the other.
R-squared is the square of the correlation coefficient. It represents the fraction of the variation in one variable that can be explained by a linear relationship with the other. An r of 0.8 gives an r² of 0.64, or 64%.
Also known as
TG we-Calculate Editorial Team. (2026). Correlation Coefficient Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/correlation-coefficient-calculator
TG we-Calculate Editorial Team. "Correlation Coefficient Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/correlation-coefficient-calculator.
TG we-Calculate Editorial Team, "Correlation Coefficient Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/correlation-coefficient-calculator
@misc{wecalculate_correlation_coefficient_calculator, title = {Correlation Coefficient Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/correlation-coefficient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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