Statistics & Probability

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Coefficient of Determination Calculator.

Calculate R² and the percentage of variance explained.

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Set your values

Results update as you type.

02 / ANSWER

Correlation r

coefficientOfDetermination

0.640000

percentExplained

64.000000

Results update automatically as you type.

Use Cases

Assess linear relationship strength

Use R² to quantify how well one variable explains the variation in another, helping you evaluate the strength of a linear association.

Example: If r = 0.7, R² = 0.49, meaning 49% of the variance is shared.

Compare model fits

When comparing different models or predictors, R² helps you see which one explains more variance, aiding in model selection.

Example: Model A has R² = 0.6, Model B has R² = 0.8, so B explains more variance.

Frequently Asked Questions

What is the coefficient of determination?: The coefficient of determination, denoted R², measures the proportion of variance in one variable that is predictable from the other variable. It ranges from 0 to 1, with higher values indicating a stronger linear relationship.
How do I calculate R² from correlation?: Simply square the correlation coefficient (r). For example, if r = 0.8, then R² = 0.64. This calculator does that for you instantly.
What does an R² value of 0.5 mean?: An R² of 0.5 means that 50% of the variance in one variable is explained by the other variable. The remaining 50% is due to other factors or random variation.

Tips & Common Mistakes

Tips

Ensure your correlation r is between -1 and 1. If it's outside this range, double-check your calculation.
R² is always non-negative, even if r is negative. Squaring removes the sign.
Use R² as a relative measure; it doesn't indicate causation or the slope of the relationship.
For a quick check, remember that R² = r². You can verify the calculator's output manually.

Common Mistakes to Avoid

Forgetting to square the correlation coefficient, leading to an incorrect R² value.
Using the absolute value of r instead of squaring it, which gives the same result but may confuse interpretation.
Interpreting R² as the percentage of data points that fit the line, when it actually represents variance explained.

Last updated: August 13, 2026

Use Cases

Assess linear relationship strength

Use R² to quantify how well one variable explains the variation in another, helping you evaluate the strength of a linear association.

Example: If r = 0.7, R² = 0.49, meaning 49% of the variance is shared.

Compare model fits

When comparing different models or predictors, R² helps you see which one explains more variance, aiding in model selection.

Example: Model A has R² = 0.6, Model B has R² = 0.8, so B explains more variance.

Frequently Asked Questions

What is the coefficient of determination?

The coefficient of determination, denoted R², measures the proportion of variance in one variable that is predictable from the other variable. It ranges from 0 to 1, with higher values indicating a stronger linear relationship.

How do I calculate R² from correlation?

Simply square the correlation coefficient (r). For example, if r = 0.8, then R² = 0.64. This calculator does that for you instantly.

What does an R² value of 0.5 mean?

An R² of 0.5 means that 50% of the variance in one variable is explained by the other variable. The remaining 50% is due to other factors or random variation.

Tips & Common Mistakes

Tips

Ensure your correlation r is between -1 and 1. If it's outside this range, double-check your calculation.
R² is always non-negative, even if r is negative. Squaring removes the sign.
Use R² as a relative measure; it doesn't indicate causation or the slope of the relationship.
For a quick check, remember that R² = r². You can verify the calculator's output manually.

Common Mistakes to Avoid

Forgetting to square the correlation coefficient, leading to an incorrect R² value.
Using the absolute value of r instead of squaring it, which gives the same result but may confuse interpretation.
Interpreting R² as the percentage of data points that fit the line, when it actually represents variance explained.

Use Cases

Assess linear relationship strength

Use R² to quantify how well one variable explains the variation in another, helping you evaluate the strength of a linear association.

Example: If r = 0.7, R² = 0.49, meaning 49% of the variance is shared.

Compare model fits

When comparing different models or predictors, R² helps you see which one explains more variance, aiding in model selection.

Example: Model A has R² = 0.6, Model B has R² = 0.8, so B explains more variance.

Frequently Asked Questions

What is the coefficient of determination?

How do I calculate R² from correlation?

Simply square the correlation coefficient (r). For example, if r = 0.8, then R² = 0.64. This calculator does that for you instantly.

What does an R² value of 0.5 mean?

An R² of 0.5 means that 50% of the variance in one variable is explained by the other variable. The remaining 50% is due to other factors or random variation.

Tips & Common Mistakes

Tips

Ensure your correlation r is between -1 and 1. If it's outside this range, double-check your calculation.
R² is always non-negative, even if r is negative. Squaring removes the sign.
Use R² as a relative measure; it doesn't indicate causation or the slope of the relationship.
For a quick check, remember that R² = r². You can verify the calculator's output manually.

Common Mistakes to Avoid

Forgetting to square the correlation coefficient, leading to an incorrect R² value.
Using the absolute value of r instead of squaring it, which gives the same result but may confuse interpretation.
Interpreting R² as the percentage of data points that fit the line, when it actually represents variance explained.