About Pearson Correlation Calculator
This Pearson correlation calculator measures the strength and direction of the straight-line relationship between two numeric variables. It opens on Anscombe set I and shows r, r², the t test and a Fisher z interval. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Pearson r is the covariance of x and y divided by the product of their standard deviations. It is unchanged if you rescale or shift either variable, so r for heights in inches equals r for heights in centimetres.
It assumes the relationship is roughly linear and that there are no extreme outliers. For the p-value to be exact the pairs should be independent and roughly bivariate normal. If these fail, check the Spearman page.
How to use Pearson Correlation Calculator
- Paste your data as two columns from a spreadsheet, or type one x, y pair per line. Use the "Two columns" tab if your x and y values are in separate lists.
- Pick the headline coefficient: Pearson r, Spearman ρ or Kendall τ-b. All three are always shown in the table.
- Choose a confidence level for the interval of r. 95% is the usual choice.
- Read the strength and direction sentence, the p-value and the confidence interval. A small p-value means the correlation is unlikely to be zero in the population.
- Check the scatter plot for curves, clusters or outliers, because one number can hide them.
- Open the step-by-step panel to see the means, the sums of squares, r, the t statistic and the Fisher z interval.
Features
- Pearson r with a t test for H0: ρ = 0 and a Fisher z confidence interval.
- Spearman rank correlation with tied values given their average rank.
- Kendall τ-b, corrected for ties, with a normal approximation for p.
- Paste from Excel or Google Sheets: tab, comma, semicolon and space separated pairs all work, and decimal commas are understood.
- Scatter plot with a least squares trend line, a values table for screen readers and a PNG download.
- Strength and direction in plain words, plus r² for Pearson.
- Worked Pearson steps in KaTeX that you can copy as LaTeX.
- Four bundled examples, including Anscombe set I and a data set with an outlier.
Pearson r and its test
The test statistic follows a t distribution with n - 2 degrees of freedom when the true correlation is zero.
r = Σ(x − mean x)(y − mean y) / sqrt(Σ(x − mean x)² × Σ(y − mean y)²)
t = r × sqrt(n − 2) / sqrt(1 − r²)Worked examples
Anscombe's quartet, set I (11 pairs) gives r = 0.8164, r² = 0.6665
p = 0.00217 and the 95% interval for r runs from 0.424 to 0.951.
Privacy: how it works
- Everything is calculated by code running in your browser tab. Your data is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Always look at the scatter plot. A curve, two clusters or one outlier can make r misleading.
- If r is near zero but the plot shows a clear curve, the relationship is real but not linear.
- With many pairs, even a tiny r can be significant. Judge the size of r, not only the p-value.
- Do not include totals or averages of the same variable twice. Repeated measures break the independence that the p-value assumes.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your pairs are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your pairs are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does r² mean?
r² is the share of the variation in y that a straight line on x accounts for. An r of 0.816 gives r² of 0.666, so about two thirds of the variation.
Does Pearson r need normal data?
The coefficient itself does not. The p-value and confidence interval work best when the pairs are roughly bivariate normal, especially for small samples.
Why is r undefined for my data?
If every x or every y is the same, there is no spread to compare and r is not defined. The calculator tells you which column is constant.
More Correlation Coefficient Calculator pages
- Correlation Coefficient CalculatorPaste two columns or x, y pairs to get Pearson r, Spearman ρ and Kendall τ with a scatter plot and the working.
- Spearman Rank Correlation CalculatorPaste x, y pairs to get Spearman ρ, which resists outliers and measures any steady rise or fall.
- Kendall Tau Correlation CalculatorPaste x, y pairs to get Kendall τ-b, built from concordant and discordant pairs.