What does R² tell me?

R² is the proportion of variance in y explained by a linear relationship with x. R² = 0.73 means 73% of the variation in y is associated with x.

Why might a high r not be significant?

Because significance depends on sample size too. A correlation of 0.85 with only n = 5 has just df = 3 and can fall short of the t-critical even though r looks impressive.

Does Pearson r detect non-linear relationships?

No — only linear. Two variables can have r ≈ 0 yet still be perfectly related through a non-linear curve. Always plot the data.

What if every x or every y is identical?

Sxx or Syy is zero, the denominator collapses, and r is undefined. The calculator returns 0 with the implication that there is no usable variation.

Is this Pearson or Spearman?

Pearson. For ranks (Spearman), apply the same calculator after converting each column to ranks.

Correlation Calculator

Compute Pearson r, R², covariance, and the two-tailed significance test from any list of (x, y) pairs.

Written by Golam Rabbani, Founder & Lead Engineer

This interactive tool requires JavaScript. Read the formula and worked example below; you can compute the result by hand.

How to use this correlation calculator

Paste your (x, y) pairs one per line — comma or space separated.
Press Calculate to compute Pearson r, R², covariance, and the significance test.
Check the table for the t statistic and the bundled t-critical at α = 0.05.
Copy the result or Reset to clear the data.

About this correlation calculator

Pearson's correlation coefficient r measures the strength and direction of a linear relationship between two variables. r ranges from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). The calculator uses sample means and (n − 1)-divisor standard deviations, then converts r into a t statistic with df = n − 2 to test whether the population correlation differs from zero: t = r · √(df) / √(1 − r²). The two-tail critical value at α = 0.05 comes from the bundled t-table, so significance is decided locally without any network lookup.

Worked example. Enter the pairs (1, 2), (2, 4), (3, 5), (4, 4), (5, 6). x̄ = 3, ȳ = 4.2. Sxx = 10, Syy = 8.8, Sxy = 8. So r = 8 / √(10 · 8.8) = 8 / √88 ≈ 0.8528, R² ≈ 0.7273. With df = 3, t = 0.8528 · √3 / √(1 − 0.7273) = 1.4771 / 0.5222 ≈ 2.828. The bundled t-critical at α = 0.05, df = 3 is 3.182, so |t| < 3.182 — fail to reject H₀: ρ = 0 at the 5% level despite the strong-looking r, because n is tiny. The tool reports all of this in one table.

FAQ

What does R² tell me?: R² is the proportion of variance in y explained by a linear relationship with x. R² = 0.73 means 73% of the variation in y is associated with x.
Why might a high r not be significant?: Because significance depends on sample size too. A correlation of 0.85 with only n = 5 has just df = 3 and can fall short of the t-critical even though r looks impressive.
Does Pearson r detect non-linear relationships?: No — only linear. Two variables can have r ≈ 0 yet still be perfectly related through a non-linear curve. Always plot the data.
What if every x or every y is identical?: Sxx or Syy is zero, the denominator collapses, and r is undefined. The calculator returns 0 with the implication that there is no usable variation.
Is this Pearson or Spearman?: Pearson. For ranks (Spearman), apply the same calculator after converting each column to ranks.