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Coefficient of Determination (R²) Calculator

From r to R² in one step.

Result

0.4900
49.00%

How it is calculated

Enter the Pearson correlation coefficient r, a number from −1 to 1, with a decimal point. The tool squares it: R² = r × r, shown to 4 decimals, and also as a percentage, R² × 100, labelled as the explained variance. Because squaring removes the sign, r = 0.7 and r = −0.7 give the same result. Values outside −1 to 1 return no result, since a correlation cannot exceed those limits. This is the R² of a simple, one-predictor linear regression; for a model with several predictors, or an adjusted R², you need the regression output itself.

Worked example

Suppose a study reports a correlation of r = 0.7 between hours of practice and a test score. Square it: 0.7 × 0.7 = 0.4900. As a percentage, 0.49 × 100 = 49.00%. So the straight-line relationship accounts for 49% of the variation in test scores, and the remaining 51% is explained by other factors or random variation. Entering r = −0.7 for an inverse relationship would give exactly the same figures.

Try this example →

Common mistakes

  • Reading r = 0.7 as "70% explained". The share of variance explained is r², here 49%, which is why a seemingly strong correlation can still leave half the variation unexplained.
  • Entering R² itself into the box. The field expects r; entering 0.49 would return 0.2401, a square of a square.
  • Dropping the minus sign and treating the result as if it kept the direction. R² is always 0 to 1 and says nothing about whether the relationship is positive or negative.
  • Treating a high R² as proof of causation, or applying it to a curved relationship. It measures only how well a straight line fits.

About this calculator

The coefficient of determination, R², is simply the square of the Pearson correlation coefficient r, but squaring it changes its meaning in an important way: r tells you the strength and direction of a linear relationship, while R² tells you the percentage of variance in the outcome variable that is explained by the predictor. An r of 0.7 sounds strong, but R² = 0.49 reveals that only 49% of the variation is actually accounted for by the model — the rest is noise or other factors.

Statisticians and researchers report R² alongside every simple linear regression to communicate model fit in a way non-technical readers can grasp as a percentage. Financial analysts use it to measure how closely a stock or fund’s returns track a benchmark index (a high R² means the fund’s performance is largely explained by the market, useful for spotting closet-indexing), and data scientists use it as a baseline metric when evaluating whether a regression model is worth deploying.

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