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Correlation and Regression

Coefficient of Determination Calculator

Use this coefficient of determination calculator to find R² from summary data or paired raw data. Get the percentage of variation accounted for and a clear step-by-step solution.

Enter a value from −1 to 1.
Enter the variation accounted for by the regression model.
Enter the total variation in the response variable.
Enter the variation not accounted for by the regression model.
Enter the total variation in the response variable.
Separate values using commas, spaces, tabs, or new lines.
Enter the Y values in the same paired order as the X values.

How to Use the Coefficient of Determination Calculator

This calculator helps you find the coefficient of determination (R2) from summary or raw data.

To use the calculator:

  1. Select the Summary Data or Raw Data Option. The Summary Data option helps you to find the coefficient of determination (R2) either from the Pearson’s correlation coefficient (r), Regression Sum of Squares (SSR), and Total Sum of Squares (SST), or from Error Sum of Squares (SSE) and Total Sum of Squares (SST). On the other hand, with the Raw Data option, you can quickly find the coefficient of determination (R2) from X values and Y values.
  2. Enter the data. For the Summary Data option, select the available summary data options (r, SST and SSE, or SSR and SST) and enter the known values. However, for the Raw Data option, you can copy-paste values from Excel, Google Sheets, or text documents, or enter values manually and separate them using commas, spaces, line breaks, or tabs.
  3. Click calculate

The calculator will instantly return the coefficient of determination (R2) and show you how the value was calculated from the entered values, step-by-step.

What Is the Coefficient of Determination?

The coefficient of determination, written as R² and read as “R-squared,” is a statistical measure that shows the proportion of variation in a dependent variable that is accounted for by the independent variable in a linear relationship or regression model. It is mainly expressed as a percentage.

For example, an R2 of 0.68 implies that about 68% of the variation in the dependent variable is explained by the independent variable (s) in the model, while the remaining 32% is unexplained.

Coefficient of Determination Formula

The coefficient of determination formula varies depending on the available information. You can compute it from Pearson’s correlation, regression sum of squares and total sum of squares, as well as error sum of squares and total sum of squares.

In this section, you’ll learn how to find the coefficient of determination (R2) using the most common formulas.

1) Pearson’s r

To find the Coefficient of determination from Pearson’s correlation coefficient (r), simply square the value. Thus, the formula is:

Coefficient of Determination, R2 = r2

Where:

  • r is Pearson’s correlation coefficient.

Tip. You should only use this formula whenever you want to find the coefficient of determination after finding the correlation coefficient or fitting a simple linear regression.

Don’t know how to find Pearson’s correlation coefficient? Use the correlation coefficient calculator to get instant results and learn how to find the value manually.

Example 1: Finding R² from Pearson’s r

A researcher examines the relationship between employee stress and job satisfaction. The analysis gives a Pearson correlation coefficient of: r = −0.73. Calculate the coefficient of determination.

Solution

By definition, the coefficient of determination, R2 = r2

From the question, the correlation coefficient, r = -0.73. Substituting the value into the formula gives:

R2 = (-0.73)2

= 0.5329

This implies that about 53.29% of the variation in job satisfaction is explained by employee stress.

Alternatively, you can quickly find the same results using the coefficient of determination calculator and following these simple steps:

  1. Select the Summary Data option
  2. Choose Pearson’s r as the available information
  3. Enter -0.73 in the Pearson’s correlation input field
  4. Click Calculate

The calculator will instantly return R2 and show you how the value was obtained using a step-by-step approach.

2) SSR and SST

If you know the regression sum of squares (SSR) and total sum of squares (SST), the coefficient of determination formula is:

Coefficient of Determination, R2 = SSR / SST

Where:

  • SSR is the regression sum of squares.
  • SST is the total sum of squares.

SSR represents the variation accounted for by the regression model, while SST represents the total variation in the dependent variable.

Example 2: Finding R² from SSR and SST

A regression model is used to predict monthly sales from advertising expenditure. The regression output gives SSR = 189 and SST = 270. Calculate the coefficient of determination.

Solution

By definition, given SSR and SST, the coefficient of determination formula is: R2 = SSR / SST

Substituting the values into the formula, we get:

R2 = 189/270

= 0.70

This implies that about 70% of the variation in monthly sales is accounted for by the advertising expenditure.

You can also get similar results using our calculator. Just follow these steps:

  1. Select the Summary Data option
  2. Select SSR and SST as the available information.
  3. Enter 189 for SSR and 270 for SST.
  4. Click Calculate.

The calculator will instantly return the coefficient of determination as R² = 0.7 and show the steps.

3) SSE and SST

When the error sum of squares and total sum of squares are known, the coefficient of determination formula becomes:

Coefficient of Determination, R2 = 1 − (SSE / SST)

Where:

  • SSE is the error sum of squares.
  • SST is the total sum of squares.

The ratio SSE / SST represents the proportion of variation not accounted for by the model. Subtracting this value from 1 gives the proportion accounted for by the model.

Example 3: Finding R² from SSE and SST

A researcher uses a regression model to predict blood pressure from age. The regression output gives SSE = 52 and SST = 208. Calculate the coefficient of determination.

Solution

By definition, the coefficient of determination when SSE and SST are known is: R2=1−SSE​/SST. Substituting the values gives:

R2=1−52/208

=0.75

This implies that the regression model accounts for 75% of the total variation in blood pressure.

However, if you want to quickly find R2 from SSE and SST without manual computations, you can use our calculator and follow these steps:

  1. Select the Summary Data option.
  2. Select SSE and SST as the available information
  3. Enter 52 as SSE and 208 as SST in the input fields
  4. Click Calculate.

The calculator will instantly yield the same coefficient of determination value and show you how to find it manually.

4) Coefficient of Determination from Raw Data

Whenever you want to calculate the coefficient of determination from raw data, you’ll need to first calculate Pearson’s correlation coefficient and then square the results.

The correlation coefficient formula is: r = Cov(X, Y) / (sx × sy)

Where:

  • Cov(X, Y) is the covariance between X and Y.
  • sx is the standard deviation of X values.
  • sy is the standard deviation of Y values.

Struggling to find the correlation coefficient (r) manually? Visit the correlation coefficient page for more details.

Our coefficient of determination calculator also allows you to find R2 from raw data. To use the calculator:

  1. Select the Raw Data option
  2. Enter the raw data values in the X and Y input fields. You can copy-paste values directly from Excel, Google Sheets, or text documents. However, for manual data entry, make sure to separate values using commas, spaces, tabs, or line breaks.
  3. Click calculate

The calculator will instantly return the coefficient of determination and show you how to find it manually.

Frequently Asked Questions

What does R-squared mean?

R-squared measures the proportion of variation in a dependent variable accounted for by a regression model or linear relationship. For example, R2=0.72 means the model accounts for 72% of the variation in the dependent variable

How do I calculate R² from r?

To find the coefficient of determination (R2) from the correlation coefficient (r), simply square the correlation value.

How do I calculate R² from SSR and SST?

To find the coefficient of determination from SSR and SST, divide the regression sum of squares (SSR) by the total sum of squares (SST). That is, R² = SSR​/ SST, where SSR is the regression sum of squares and SST is the total sum of squares.

How do I calculate R² from SSE and SST?

To find the coefficient of determination from SSE and SST, divide SSE by SST and subtract the result from 1. That is, R2=1−SSE/SST​

Can R² be greater than 1?

Under the standard in-sample regression formulas used by this calculator, R² lies between 0 and 1. Values outside this range may arise under different definitions, models without an intercept, or some out-of-sample calculations.

Does a high R² mean the model is statistically significant?

Not necessarily. Statistical significance depends on additional information, including the sample size, number of predictors, test statistic, and significance level.

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Mburu, J.. (2026, August 5). Coefficient of Determination Calculator. StatCalc.net. Retrieved August 25, 2026, from https://statcalc.net/coefficient-of-determination-calculator/
Joseph Mburu

About This Calculator

Prepared by Joseph Mburu · Updated on

Joseph is an applied statistician and data analyst with over 6 years of experience helping students, researchers, and professionals solve statistics and data analysis problems. He holds a degree in Applied Statistics and a Master’s degree in Data…

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