Correlation Calculator – Calculate Pearson's Correlation Coefficient

Correlation Calculator

Enter two lists of paired values, and this calculator returns Pearson's correlation coefficient (r) — a single number from -1 to 1 that captures how strongly, and in what direction, the two variables move together in a straight-line pattern.

Formula

r = (n·Σxy − Σx·Σy) / √((n·Σx² − (Σx)²)(n·Σy² − (Σy)²)). The numerator compares how x and y vary together; the denominator normalizes that against how much each variable varies on its own, which is what keeps the result bounded between -1 and 1 regardless of the scale of the original data.

For the pairs (1,2), (2,4), (3,5), (4,4), and (5,5), that formula works out to r ≈ 0.775 — a fairly strong positive relationship, meaning as x increases, y tends to increase too, in a reasonably linear pattern.

Reading the number

Values near +1 mean a strong positive linear relationship — as one variable increases, the other reliably increases too. Values near -1 mean a strong negative relationship — one increases as the other decreases. Values near 0 mean little to no linear relationship, though the variables could still be related in a curved or more complex way that a straight-line measure like this one won't pick up.

Correlation isn't causation, and it isn't the whole story

A high correlation coefficient shows that two variables tend to move together — it says nothing about whether one causes the other. Both could be driven by some third factor, or the relationship could simply be coincidental in a small sample. It's also worth remembering Pearson's r only measures linear association: two variables with an obvious curved relationship (like a U-shape) can still produce a correlation near 0, so it's worth looking at a scatter plot alongside this number whenever you can.