Correlation Calculator

How to use

1. 1Paste your paired data into the textarea, one (x, y) pair per line. Use a comma, space, tab, or semicolon between x and y. An optional header row like 'x, y' or 'hours, score' is skipped automatically.
2. 2Or click an example dataset (Study hours vs exam score, Price vs demand, Height vs shoe size, Random scatter) to load a starter set and replace whatever is in the textarea.
3. 3Read the three coefficients in the Correlation coefficients panel: Pearson r for linear association, Spearman rho for monotonic association on ranks, and Kendall tau-b for pair concordance with tie correction. Each shows R-squared or t/z, the p-value, and a plain-English strength label.
4. 4Use the Significance decision panel to see the reject or fail-to-reject verdict at alpha 0.10, 0.05, and 0.01 for each coefficient (two-tailed test of zero correlation).
5. 5Check the scatter plot to see the shape and direction of the relationship. The dashed line is the least-squares fit. Read the descriptive statistics for n, mean, SD, min, and max on each variable.
6. 6Click Copy summary for a one-paragraph readout or Copy full report for the complete breakdown to paste into homework, a spreadsheet, or a launch doc.

About this tool

Correlation Calculator returns the three correlation coefficients used in almost every statistics course and applied analysis on paired (x, y) data: Pearson r for linear association, Spearman rho for monotonic association on ranks, and Kendall tau-b for concordance between pairs with the standard tie correction. Paste any number of (x, y) pairs (3 to 5,000), one pair per line, separated by commas, spaces, tabs, or semicolons, with an optional header row like 'x, y' that is detected and skipped automatically. The result panel updates instantly with each coefficient to four decimal places, an interpretive strength label (very weak, weak, moderate, strong, very strong, near-perfect), the coefficient of determination R-squared for Pearson, the t statistic on n - 2 degrees of freedom with a two-tailed p-value for both Pearson and Spearman, the z statistic and normal-approximation p-value for Kendall, the count of concordant, discordant, and tied pairs (in x, in y, and in both), and a 95% confidence interval for the Pearson r computed with the Fisher z transformation (z = atanh(r), SE = 1 / sqrt(n - 3), back-transformed with tanh). A significance verdict at alpha 0.10, 0.05, and 0.01 is shown for each coefficient, and a live SVG scatter plot draws every point with the least-squares regression line dashed across the chart, so the shape, direction, and strength of the relationship are visible at a glance. Descriptive statistics (n, sample mean, sample SD with the n - 1 Bessel correction, min, max) for both variables and the best-fit line equation y = b0 + b1 x are reported alongside, so a single paste covers the descriptive, inferential, and graphical pieces of a correlation write-up. Numerically, the Pearson and Spearman p-values use the regularized incomplete beta function via the Lentz continued fraction with a Lanczos log-gamma backbone (accurate to roughly 1e-12), and the Kendall p-value uses the standard no-ties normal approximation z = tau / sqrt(2(2n + 5) / (9n(n - 1))) which matches scipy.stats.kendalltau closely when ties are modest. All three coefficients run in a single pass, so a 1,000-pair paste resolves in milliseconds. Useful for AP Statistics and college statistics homework, psychology, education, biology, ecology, finance, and marketing research, sanity-checking the correlation matrix from R, Python, or Excel, picking the right coefficient when the relationship is non-linear (Spearman) or ordinal (Kendall), and any time you need a defensible report on how two measurements move together. Pair this tool with the Linear Regression Calculator when you also want the residuals and standard errors of the OLS slope, with the P-Value Calculator when you have a coefficient in hand and need only the p-value, with the T-Test Calculator when you are comparing two group means instead of two paired measurements, or with the Confidence Interval Calculator when the question is interval estimation without a hypothesis test. Everything runs locally in your browser, so the paired data you paste here is not uploaded.

Free to use. Works in your browser. No signup, no login.