Statistics & Probability calculator
Correlation Coefficient Calculator
Calculate Pearson and Spearman correlation coefficients from paired data, then review |r|, R², scatter plots, regression summaries, and step-by-step work.
Correlation coefficient calculator results
Your correlation result will appear here
Enter paired data and click Calculate.
Correlation coefficient
Scatter plot
Pearson correlation measures linear association, while Spearman correlation measures rank-based monotonic association. Correlation does not imply causation.
Calculator overview
Quick Correlation Coefficient Calculator Overview
Use this correlation coefficient calculator to find Pearson correlation, Spearman rank correlation, absolute correlation, R squared, covariance, and optional regression summary from paired data. It keeps Pearson and Spearman meanings separate.
Enter paired x and y values to calculate correlation, R squared, and supporting statistics.
Guide
Correlation Coefficient Calculator Guide
Use this guide to understand Pearson r, Spearman rank correlation, absolute correlation, R², and the limits of interpreting association from paired data.
What This Calculator Does
This correlation coefficient calculator helps users calculate Pearson and Spearman correlation coefficients from paired x and y data. It supports pasted paired rows, separate x and y lists, and a two-column data table.
The page keeps the coefficient first, then adds |r|, R², optional scatter plots, a compact regression summary, covariance, means, standard deviations, and step-by-step work where useful.
What the Correlation Coefficient Means
A correlation coefficient measures the strength and direction of association between two variables. Values range from -1 to +1. A positive value means y tends to increase as x increases. A negative value means y tends to decrease as x increases. A value near 0 means little linear association.
Pearson vs Spearman Correlation
Pearson correlation measures linear association using the original numeric values. It is the default mode because many users want to calculate Pearson correlation or compute the sample correlation coefficient r.
Spearman correlation converts the data to ranks first. It is often better for ranked data or monotonic patterns that are not perfectly linear. Ties matter in Spearman calculations, so this calculator assigns tied values their average ranks.
Absolute Value of the Correlation Coefficient
The absolute value of the correlation coefficient, |r|, removes the direction and keeps only the strength. For example, r = -0.85 and r = 0.85 have the same absolute correlation strength, but opposite directions.
Coefficient of Determination
The coefficient of determination, R², is Pearson r squared. In a simple linear summary, it describes the proportion of variation in y associated with the fitted line. It is useful, but it should still be checked with a scatter plot because non-linear patterns can be misleading.
How to Use
- 1Choose Pearson or Spearman
Use Pearson for linear association and Spearman for rank-based monotonic association.
- 2Enter paired data
Paste paired rows, separate x and y lists, or use the two-column table.
- 3Click Calculate
The page keeps results hidden until the calculator runs.
- 4Review r and R²
Check the coefficient, absolute value, R², and worked steps.
- 5Use the plot when needed
A scatter plot can reveal outliers or non-linear patterns that r alone may miss.
Tips / Notes
- Correlation does not imply causation.
- Pearson correlation is sensitive to outliers and works best for linear patterns.
- Spearman correlation is often better for ranked or monotonic data.
- A high R² can still miss important non-linear structure if the relationship is not linear.
- Ties matter in rank-based calculations and should be handled with average ranks.
FAQ
Frequently Asked Questions
Clear answers about Pearson r, Spearman ranks, absolute correlation, R², and paired-data input.
What does the Correlation Coefficient Calculator do?
It calculates Pearson correlation, Spearman rank correlation, absolute correlation, R², and optional regression summaries from paired x and y data.
How do I calculate Pearson's correlation coefficient?
Enter paired x and y values. The calculator finds the x and y means, computes centered deviations, divides the sum of deviation products by the product of the deviation sums, and returns Pearson r.
What is the difference between Pearson and Spearman correlation?
Pearson measures linear association using the raw values. Spearman ranks the values first and measures monotonic association, with tied values handled by average ranks.
What does the absolute value of the correlation coefficient mean?
|r| shows the strength of association without direction. A value near 1 is stronger, while a value near 0 is weaker.
How do I calculate the coefficient of determination?
For Pearson correlation, R² is r squared. It is shown automatically with the Pearson and regression summary modes.
Why can correlation be zero even when variables are still related?
Pearson correlation measures linear association. A curved or non-linear relationship can have r near zero even when the variables are meaningfully related.