Correlation Coefficient Calculator

This correlation coefficient calculator computes Pearson’s r and Spearman’s ρ from paired x and y values. It also reports a two-sided p-value for each coefficient and draws a scatter plot of the points. The site already has tools that convert between a covariance and r; this page is the one that starts from the raw data.

Correlation coefficient calculator

Paste paired x and y values to get Pearson’s r and Spearman’s ρ, with two-sided p-values.

Use a period for decimals. Separate values with commas, spaces, or new lines. X and Y must have the same length (at least three pairs).

Calculator loading… If the form does not return a result, wait a moment and try again.

Pearson and Spearman formulas

Pearson: r = Sxy / √(Sxx Syy), with Sxy = Σ(x − x̄)(y − ȳ).

The usual test of H₀: ρ = 0 uses t = r √((n−2)/(1−r²)) with df = n − 2.

Spearman: rank each variable, using average ranks for ties, then compute Pearson’s r on the ranks. The p-value shown here uses the same t approximation as Pearson, which is standard for a quick calculator but is an approximation, especially in small samples or with many ties.

Worked example

Using the same eight pairs as the regression example — x = 1 through 8 and y = 2.1, 3.9, 6.2, 7.8, 10.1, 11.7, 14.2, 15.8 — Pearson’s r is about 0.999 and Spearman’s ρ is 1, because the ranks increase together even though the relationship is not a perfectly straight line.

Related calculators and guides

Frequently asked questions

When should I use Spearman instead of Pearson?

Use Pearson when you want the strength of a linear relationship on the original scale. Use Spearman when you care about a monotone relationship, when the data are ordinal, or when outliers would distort Pearson’s r.

Does a significant correlation mean x causes y?

No. Correlation does not imply causation. A significant r or ρ only says the association in the sample would be unusual if there were no association in the population.

How are ties handled in Spearman’s ρ?

Tied values receive the average of the ranks they would have occupied. The coefficient is then the Pearson correlation of those average ranks.

Is this the same as the covariance-to-r calculator?

No. The older tools convert between a known covariance and a correlation coefficient. This calculator estimates r and ρ from a list of paired observations.

Can I also get the regression line?

Yes. Use the linear regression calculator with the same two lists. Its Pearson r will match the Pearson r here.