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R-Squared Calculator

Find R² from a correlation coefficient.

Result

0.6400
64.00%

How it is calculated

For a simple linear regression, the coefficient of determination equals the square of the correlation coefficient: R² = r². Enter r, a value from −1 to 1; anything outside this range gives no result. R² is shown as a decimal with four digits and as a percentage. It is the share of the variation in y that is explained by the straight-line relationship with x. Because r is squared, the sign is lost: r = −0.8 and r = 0.8 give the same R². This shortcut applies to one predictor; with several predictors R² must come from the regression output.

Worked example

The correlation between hours of practice and error rate is r = −0.8 (negative: more practice, fewer errors). R² = (−0.8)² = 0.64. The tool shows 0.6400, or 64.00%. About 64% of the variation in the error rate is accounted for by the straight-line relationship with practice, and the other 36% is left unexplained.

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Common mistakes

  • Entering R² in the r field. If you already have R² = 0.64, the correlation is 0.8, not 0.64.
  • Expecting the sign of r to survive. R² is never negative, so the direction of the relationship is lost.
  • Reading R² as proof of causation. A high value shows fit, not that x causes y.
  • Entering r as a percentage (80) instead of a value from −1 to 1.
  • Using this on a model with several predictors or a curve, where R² is not simply r².

Sources

About this calculator

This calculator squares a correlation coefficient (r) to get the coefficient of determination (R²), a statistic that expresses what proportion of the variance in one variable is explained by its linear relationship with another. An R² of 0.81, for example, means 81% of the variation in the dependent variable is accounted for by the independent variable, leaving 19% attributable to other factors or randomness.

Statisticians and data analysts evaluating how well a linear regression model fits observed data, researchers reporting the strength of a relationship in a paper, and students in statistics courses converting between r and R² for homework use this.

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Comments (1)

  • Editorial team

    Squaring shrinks moderate correlations more than people expect: r of 0.5 gives an R-squared of only 0.25, meaning a quarter of the variation is explained. At the other extreme, a high R-squared does not prove that x causes y, and it can hide a curved pattern a straight line fits poorly, so look at the scatter plot as well. What correlation values are typical for the data you work with?

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