# R-Squared Calculator Calculate coefficient of determination R squared from actual and predicted values > Canonical page: https://elysiatools.com/en/tools/r-squared-calculator - **Category:** Math & Numbers - **Keywords:** r squared, coefficient of determination, regression metrics, goodness of fit, calculator ## Overview The R-Squared Calculator is a specialized tool designed to measure the goodness of fit for regression models by calculating the coefficient of determination. By comparing actual observed data against predicted values, it quantifies how much of the variance in the dependent variable is explained by the model, providing essential metrics like R², explained variance percentage, and sum of squared errors. ## Inputs - **Actual Values** (textarea): e.g. 2, 4, 5, 4, 5 - **Predicted Values** (textarea): e.g. 2.8, 3.4, 4, 4.6, 5.2 - **Decimal Places** (number) ## When to use - Evaluating the accuracy of a linear or non-linear regression model after training. - Comparing different statistical models to determine which one better fits a specific dataset. - Validating forecasting results against historical data to assess predictive performance. ## How it works - Input your set of actual observed values and the corresponding predicted values from your model into the respective text areas. - Specify the desired number of decimal places to control the precision of the calculated results. - The tool computes the Sum of Squared Errors (SSE) and the Total Sum of Squares (SST) based on your data points. - The final R-squared value is derived using the formula 1 - (SSE/SST) and returned as a JSON object containing the variance percentage. ## Use cases - Data scientists verifying the performance of machine learning algorithms on test datasets. - Financial analysts assessing the reliability of stock price prediction models against historical trends. - Researchers measuring the strength of the relationship between variables in experimental studies. ## Frequently asked questions ### What does an R-squared value of 1.0 indicate? It indicates a perfect fit where the model explains 100% of the variance in the data. ### Can R-squared be negative? Yes, if the chosen model fits the data worse than a horizontal line representing the mean of the actual values. ### What is the difference between SSE and SST? SSE measures the deviation of predicted values from actual values, while SST measures the deviation of actual values from their mean. ### How many data points do I need? You need at least two pairs of actual and predicted values, though more points provide a more reliable metric. ### Is R-squared the same as the Correlation Coefficient? 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