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Correlation Coefficient Calculator

Calculate Pearson's correlation coefficient r and r² for paired x, y data. Get a plain-English read of the strength and direction of the linear relationship.

Enter at least 3 x, y pairs (one per line) to compute Pearson's correlation coefficient.

What is the Correlation Coefficient Calculator?

The ByteTools Correlation Coefficient Calculator computes Pearson's r for paired x/y data — the standard measure of how strongly two variables move together linearly.

  • Pearson's r from the covariance / standard-deviation formula
  • r² (coefficient of determination) included
  • Plain-English strength and direction interpretation
  • Shows means and intermediate sums Sxx, Syy, Sxy
  • Paste-friendly input straight from spreadsheet columns
  • 100% private — runs entirely in your browser

How to use the Correlation Coefficient Calculator

  1. 1

    Enter your data as one x, y pair per line (comma, space or tab separated).

  2. 2

    Read Pearson's r and the coefficient of determination r².

  3. 3

    Check the interpretation of strength and direction.

  4. 4

    Review the intermediate sums (Sxx, Syy, Sxy) to verify the working.

  5. 5

    Copy the summary with one click.

About the Correlation Coefficient Calculator

The ByteTools Correlation Coefficient Calculator computes Pearson's r for paired x/y data — the standard measure of how strongly two variables move together linearly. It uses the classic formula: the covariance of x and y divided by the product of their standard deviations, r = Sxy / √(Sxx·Syy).

Alongside r you get r² (the coefficient of determination, the share of variance in y explained by x), the means, and the intermediate sums Sxx, Syy and Sxy so you can follow the calculation. A plain-English interpretation classifies the relationship: strong, moderate or weak, positive or negative.

Paste pairs straight from a spreadsheet — one x, y pair per line. Everything is computed 100% locally in your browser; your data is never uploaded, stored or shared.

Frequently asked questions

How do you calculate the correlation coefficient?

Compute the deviations of each x and y from their means, then r = Σ(x−x̄)(y−ȳ) divided by the square root of Σ(x−x̄)² × Σ(y−ȳ)². For x = 1…5 and y = 2, 4, 5, 4, 5 this gives r = 6/√(10×6) ≈ 0.775, a fairly strong positive correlation.

What does r = 0.7 mean?

An r of 0.7 indicates a fairly strong positive linear relationship: as x rises, y tends to rise. Squaring it, r² = 0.49, meaning about 49% of the variation in y is associated with variation in x. The remaining variation comes from other factors or noise.

What is the difference between r and r²?

r measures the direction and strength of a linear relationship on a scale from −1 to 1. r² is its square, ranging 0 to 1, and states the proportion of variance in one variable explained by the other. r keeps the sign; r² does not.

Does correlation imply causation?

No. A high r shows that two variables move together, not that one causes the other. The link could run either way or be driven by a third variable. Correlation is evidence worth investigating, not proof of cause and effect.

What sample size do I need for a meaningful correlation?

With very few pairs, r is extremely unstable — with n = 3 or 4, large r values arise easily by chance. Most references suggest at least 20–30 pairs before reading much into moderate correlations. This tool requires at least 3 pairs and reports n so you can judge.

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