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Coefficient of Determination Calculator — result sheet
Square a correlation coefficient to express the proportion of linear variation represented by the fitted relationship.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: R² = r²; explained percentage = 100r².
For a simple linear relationship with an intercept, squaring r gives the coefficient of determination associated with that correlation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Correlation coefficient r — minimum -1; maximum 1
Worked example
| Input | Value |
|---|---|
| Correlation coefficient r | 0.8 |
R² = 0.64, or 64%.
Assumptions and limits
- The entered value is a Pearson correlation coefficient between −1 and 1.
- R² describes linear association and does not prove causation.
- Model fit, residuals, sampling uncertainty, and omitted variables are not assessed.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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