Correlation Coefficient Calculator
Feed in two parallel lists and get Pearson's r — a single number from −1 to 1 that says how tightly your x and y values rise and fall together.
How it works
Pearson's r compares how each x sits relative to its own average with how each paired y sits relative to its average. When highs pair with highs and lows with lows, the products pile up positive; when they swap, they turn negative.
The formula divides the summed products of those paired deviations by the square root of each list's own summed squared deviations. That division rescales everything into a tidy range from −1 to 1, no matter the units.
An r near 1 means a strong positive line, near −1 a strong negative line, and near 0 no straight-line relationship at all. So x = 1..5 paired with y = 2, 4, 5, 4, 6 lands around 0.77 — a fairly strong upward trend.
Frequently asked questions
What does the value of r actually tell me?
It measures the strength and direction of a straight-line relationship. Closer to +1 or −1 means the points hug a line tightly; closer to 0 means they scatter. The sign tells you whether y tends to rise or fall as x rises.
Does a high correlation prove one thing causes the other?
No, and this trips people up constantly. Two variables can move together because of coincidence or a hidden third factor. Correlation is strong evidence that they're linked, but establishing cause takes more than a single r value.
Why do my two lists need the same length?
Pearson's r works on paired data — each x has to match up with one y. If the lists are different lengths there's no clean way to pair them, so the calculator waits for equal counts before giving an answer.
Can r miss a real relationship?
It can. Pearson's r only detects straight-line patterns, so a strong curved relationship — say a U-shape — might show an r near zero even though the variables are clearly connected. Plotting the points is always worth a look.