Correlation Calculator

Pearson's r, and the r² that deflates it.

Pearson's r, and the r² that deflates it. Pearson's r measures how well two variables move together, from −1 to +1.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

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Correlation (r)

0.91652

very strong positive · r² = 0.84

Equationy = 1x + 1.3333

Slope1

Intercept1.333333

Correlation (r)0.916515

r² (variance explained)84%

Strengthvery strong positive

Data points6

Standard error0.91287

r² is the share of variation in y explained by x, and it is literally r squared — which is where over-claiming usually starts. A correlation of 0.92 sounds very strong, but it accounts for only 84% of the variation. The other 16% is something else. And none of this establishes causation: a strong fit is equally consistent with x causing y, y causing x, or a third factor driving both.

How the Correlation Calculator works

Pearson's r measures how well two variables move together, from −1 to +1. The number worth attending to is r², the share of variation actually explained — a correlation of 0.7 sounds strong but accounts for under half the variation.

Also known as: pearson correlation coefficient calculator · r value calculator · correlation coefficient formula · how to calculate correlation

r against r squared

Pearson's r runs from −1 to +1 and measures how tightly two variables track a straight line. r² is that number squared, and it is the share of variation in one variable that the other explains.

The gap between them is where over-claiming starts. A correlation of 0.7 sounds strong, and it is — but it accounts for 49% of the variation. More than half is something else.

What it cannot tell you

Correlation is symmetric and causation is not, so a strong r is equally consistent with x causing y, y causing x, or a third factor driving both.

It also only measures linear relationships. A perfect parabola can have a correlation near zero, because the rising and falling halves cancel — so a low r means no linear relationship, not no relationship.

And it is sensitive to outliers, particularly in small samples. A single extreme point can create or destroy an apparent correlation, which is why plotting the data matters more than computing the coefficient.

Where to go next

The Correlation question rarely arrives on its own. These are the ones that usually come with it:

Linear Regression Calculator — Line of best fit, with r² and the standard error.
Average Calculator — Mean, median, mode, range, and standard deviation.
Percentage Calculator — Every common percentage question in one place.
Age Calculator — Exact age in years, months, days, and total units.

Sources

Frequently asked questions

What is a correlation coefficient?

A measure from −1 to +1 of how closely two variables move together. +1 is a perfect rising line, −1 a perfect falling one, and 0 no linear relationship at all.

What is the difference between r and r²?

r² is r squared, and it is the share of variation in one variable explained by the other. r = 0.7 gives r² = 0.49 — under half, despite sounding strong.

Does correlation prove causation?

No. A strong correlation is equally consistent with x causing y, y causing x, or a third factor driving both. Establishing causation needs an experiment or a strong design argument.

What counts as a strong correlation?

It depends entirely on the field. Above 0.8 is strong in most contexts, but physics expects far higher and social science routinely works with far lower.

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