Coefficient of Determination Calculator
The coefficient of determination R² is a familiar measure of variance explained by a fitted model. This simple calculator derives it from a supplied Pearson correlation in the simple linear-regression case.
How to use this calculator
- Enter Pearson r between −1 and 1.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by coefficient of determination calculator
R² = r² for simple linear regression with an intercept.
- R² = r² for simple linear regression with an intercept.
- This shortcut is not appropriate for every regression model. A multivariable or no-intercept model needs R² from model predictions and the data.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
A correlation of 0.8 produces R² of 0.64.
0.8² = 0.64, or 64%.
R² is 0.64 (64%).
Understanding the result
The coefficient of determination R² is a familiar measure of variance explained by a fitted model. This simple calculator derives it from a supplied Pearson correlation in the simple linear-regression case.
This shortcut is not appropriate for every regression model. A multivariable or no-intercept model needs R² from model predictions and the data.
Important notes
This shortcut is not appropriate for every regression model. A multivariable or no-intercept model needs R² from model predictions and the data.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Can R² be negative?
Not from squaring a correlation; R² from some model definitions can be negative when model fit is worse than a baseline.
Does R² show causation?
No. It summarizes fit under a model and data definition.
How should I interpret this result?
This shortcut is not appropriate for every regression model. A multivariable or no-intercept model needs R² from model predictions and the data.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.