Boneyard Tools

Correlation Coefficient Calculator

Paste two data sets as x,y pairs to find the Pearson correlation coefficient r and r squared. r ranges from -1 (perfect inverse) to +1 (perfect direct), with 0 meaning no linear relationship.

How to find the correlation coefficient

  1. Enter your paired data, one x,y pair per line.
  2. Read off r, the strength and direction of the linear relationship.
  3. Use r squared to see the share of variance the relationship explains.

Examples

A moderately positive relationship

1,2
2,4
3,5
4,4
5,5
r = 0.774597, r squared = 0.6, n = 5

Frequently asked questions

What does the correlation coefficient mean?

Pearson r measures the strength and direction of a straight-line relationship between two variables. Values near +1 or -1 are strong; values near 0 are weak.

What is the difference between r and r squared?

r squared is simply r multiplied by itself. It is the proportion of variance in one variable explained by a linear fit to the other, always between 0 and 1.

Does correlation prove causation?

No. A high correlation shows two variables move together, but it does not prove one causes the other. A hidden third factor can drive both.

Do the two data sets need the same number of values?

Yes. Each x value must pair with exactly one y value, so the two lists must be the same length, with at least two pairs.

Is the result a sample or population correlation?

They are identical. The sample (n-1) and population (n) divisors cancel in the formula, so Pearson r is the same either way.

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