Pearson Correlation Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, on a scale from −1 to 1. For the example x=1,2,3,4,5 and y=2,4,5,4,5, the coefficient is about 0.77, indicating a fairly strong positive correlation.
Explanation
The Pearson correlation coefficient quantifies how closely two variables move together in a linear way: a value close to 1 indicates they increase together in near-proportional fashion, a value close to −1 indicates one increases as the other decreases, and a value close to 0 indicates no detectable linear relationship between them. The calculation relies on the covariance of the two series (how they vary together relative to their respective means), divided by the product of their individual standard deviations — this division is precisely what makes the result independent of each variable's units and scale, unlike raw covariance. A mathematical property guarantees this coefficient always stays between −1 and 1 (the Cauchy-Schwarz inequality): the extreme values only occur when the (x, y) points are exactly aligned on a line, increasing for r=1 or decreasing for r=−1. One essential point to keep in mind: a strong correlation never proves a cause-and-effect link between the two variables — two phenomena can vary together without either causing the other, for example because a third variable influences both, or by pure coincidence in a limited sample. This calculator complements our standard error of the mean calculator and our coefficient of variation calculator, two other descriptive statistics tools on this site that focus on a single series rather than a relationship between two series.
Example: x=1,2,3,4,5 and y=2,4,5,4,5
Inputs
Pairs (x, y): (1,2), (2,4), (3,5), (4,4), (5,5).
Calculation
Means: x̄=3, ȳ=4. After calculating the covariance and the variance of each series, r = covariance ÷ (standard deviation of x × standard deviation of y) ≈ 0.7746.
Result
These two series show a fairly strong positive correlation (r ≈ 0.77), without being perfectly aligned.
Frequently asked questions
Is a correlation of 0.77 considered strong?
There's no strict universal threshold, but common benchmarks consider an absolute value above 0.7 to reflect a fairly strong linear relationship, between 0.3 and 0.7 a moderate relationship, and below 0.3 a weak or negligible one. The exact interpretation, however, depends a lot on the field of study: a correlation of 0.3 can be considered notable in some research fields, and negligible in others.
Why is it said that correlation doesn't imply causation?
Because a high correlation between two variables can have several origins: one may indeed cause the other, but they could also both be influenced by a hidden third variable, or the correlation could be purely coincidental in a limited sample. The classic example is the correlation between ice cream sales and drownings: both rise in summer, without either causing the other — summer temperature explains both at once.
Does this coefficient detect every kind of relationship between two variables?
No, Pearson's coefficient only measures linear relationships (points broadly aligned on a straight line). Two variables can be very strongly linked by a nonlinear relationship (curved, for example) while still giving a Pearson coefficient close to 0, simply because that relationship doesn't have the shape of a line. Other coefficients, like Spearman's, are better suited for detecting monotonic but nonlinear relationships.