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Math & Statisticsstatistics

Correlation Coefficient Calculator

Pearson correlation between two variables, with R squared and a caution about sample size. Correlation measures straight-line association only, and a strong curved relationship can show r near zero.

Also called: pearson r calculator, correlation calculator.

Separate values with commas or spaces.

Separate values with commas or spaces.

Correlation coefficient
0.88

r is 0.88, which is strong. It explains 77.14% of the variation. Correlation is not causation, and with only 6 pairs this is far too few to be reliable.

R squared
0.77
Variation explained
77.14%
Pairs
6
Covariance
2.7
Strength
strong
On the sample size
far too few to be reliable
How this is calculated
Method and background

How this is calculated

Covariance measures whether two variables move together, and dividing by both standard deviations normalises it to between minus one and one so it can be compared across datasets. R squared is the share of variation in one variable explained by the other. Two limits matter: it only detects linear association, so a perfect parabola scores near zero, and on a handful of points a high r is entirely consistent with no relationship at all.

Pearson correlation: covariance normalised by both standard deviations
x, y
The paired values
r
Correlation, between -1 and 1

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a positive association

X values
1, 2, 3, 4, 5, 6
Y values
2, 4, 5, 4, 5, 7

Correlation coefficient0.88

Computed independently from the Pearson formula

Open this example

a perfect line has r of one

X values
1, 2, 3, 4
Y values
2, 4, 6, 8

Correlation coefficient1

boundary: the definitional case

Open this example

Method and limits

What it assumes

  • Paired observations of equal length.

What it deliberately does not model

  • Linear association only. A strong non-linear relationship can produce r near zero.
  • Extremely sensitive to outliers. One point can create or destroy an apparent correlation.
  • It says nothing about causation, and never will.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What counts as a strong correlation?
It depends entirely on the field. Above 0.7 is strong in most social science and unremarkable in physics. The sample size matters more than the threshold.
Can r be zero when the variables are clearly related?
Yes. Pearson only measures straight-line association, so a perfect U-shaped relationship scores near zero. Plot the data before trusting the number.