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CORRELATION COEFFICIENT CALCULATOR

Correlation calculator: Pearson, Spearman, and Kendall.

Paste paired X and Y values to get the correlation coefficient, p value, 95% confidence interval, r², the regression line, a scatter plot, and an APA-style sentence.

DATA

One X Y pair per line

BROWSER-ONLY

Paste two columns from Excel, SPSS, or Google Sheets: X then Y on each line, separated by a space, comma, or tab. A header row is skipped automatically.

METHOD

Correlation coefficient formulas, interpretation, and APA reporting

Pearson, Spearman, or Kendall?

  • Pearson r: both variables numeric, a straight-line relationship, no extreme outliers (e.g. study hours and exam score)
  • Spearman rho (rₛ): ordinal data such as Likert items or ranks, skewed variables, or a curved but consistently rising or falling relationship
  • Kendall tau-b (τb): small samples or many tied ranks; it is more conservative than Spearman and has a cleaner interpretation
  • Two categorical variables? Use a chi-square test and Cramér's V instead of a correlation

Pearson correlation formula

r = Σ(x − x̄)(y − ȳ) ÷ √[Σ(x − x̄)² · Σ(y − ȳ)²], t = r·√(n − 2) ÷ √(1 − r²), df = n − 2

The p value comes from the t distribution with n − 2 degrees of freedom. The 95% confidence interval uses Fisher's z transformation: z = atanh(r), SE = 1 ÷ √(n − 3), then back-transformed with tanh.

Spearman and Kendall

rₛ = Pearson r computed on the ranks of X and Y (ties get average ranks)

Spearman's p value uses the same t approximation as Pearson, which is what SPSS reports. Kendall's tau-b counts concordant and discordant pairs, corrects for ties in both variables, and is tested with a normal (z) approximation.

How to interpret the correlation coefficient

  • |r| < .10: negligible
  • .10 to .29: weak (small)
  • .30 to .49: moderate (medium)
  • .50 to .69: strong (large)
  • .70 and above: very strong
  • The sign gives the direction: positive means both rise together; negative means one rises as the other falls. r² is the proportion of variance the two variables share.

How to report it (APA style)

“A Pearson correlation showed a strong positive relationship between study hours and exam score, r(10) = .97, p < .001, 95% CI [.89, .99].” Report the coefficient without a leading zero, the degrees of freedom (N − 2) in brackets, the exact p value, and ideally the confidence interval. For Spearman write rₛ(10) = .97; for Kendall write τb = .89.

References

  • Pearson, K. (1895). Notes on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240–242.
  • Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15(1), 72–101.
  • Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1–2), 81–93.
  • Bonett, D. G., & Wright, T. A. (2000). Sample size requirements for estimating Pearson, Kendall and Spearman correlations. Psychometrika, 65(1), 23–28.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.

ABOUT THIS TOOL

Correlation Coefficient Calculator

Measure the strength and direction of a relationship between two variables, with the right coefficient for your data, a confidence interval, a scatter plot with the regression line, and a ready APA sentence.

  • Test whether two survey scales or variables are related in a thesis
  • Use Spearman's rho for Likert items, ranks, or skewed data
  • Get r with a 95% CI and APA sentence for a results chapter

KEY FUNCTIONS

Pearson r, Spearman rho, and Kendall tau-bExact t-based p value and Fisher z 95% CIr², means, SDs, and the least-squares lineScatter plot of your dataAPA 7 report sentence
Browse research statistics & survey tools →

LEARN THE METHOD

Guides for this calculator workflow

GUIDEHow to report a correlation in APA styleAPA templates for Pearson r, Spearman rho, and Kendall tau with df, p, 95% CI, and a correlation matrix layout.Read →GUIDEHow to report regression results in APA styleAPA templates for simple and multiple regression: F, R², adjusted R², B, β, t, p, and CIs, with a coefficients table layout.Read →GUIDEHow to choose a statistical testSeparate descriptive statistics, t-tests, correlation, and one-way ANOVA by the question and data type.Read →

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