R-Squared Calculator

R-Squared, also called the Coefficient of Determination, is a statistical measure that indicates how well a regression model fits the observed data. It ranges from 0 to 1, where 1 means the model perfectly explains the variability in the data and 0 means it explains none of it.

R is the Pearson Correlation Coefficient and measures the strength and direction of the linear relationship between two variables, ranging from -1 to +1. R² is simply R squared — it represents the proportion of variance in the dependent variable (Y) explained by the independent variable (X), and is always between 0 and 1.

R² is calculated using the formula: R² = [NΣxy − ΣxΣy]² / {[NΣx² − (Σx)²][NΣy² − (Σy)²]}. First the correlation coefficient r is derived, and then it is squared to give R². This tool computes all intermediate sums automatically from your input data.

A good R² value depends on the field of study. In hard sciences, values above 0.90 are common. In social sciences, values of 0.50–0.70 may be considered acceptable. Generally, the closer R² is to 1, the better the regression model fits the data.

The Pearson r can range from -1 to +1, but R² (r squared) is always between 0 and 1 by definition when computed from the correlation coefficient. However, in some regression contexts where the model performs worse than a horizontal mean line, an adjusted or alternate formulation of R² can yield negative values.

Enter your X values in the first field and Y values in the second field, separated by commas, spaces, or new lines. Make sure both fields have the same number of values. The calculator will automatically compute R², the correlation coefficient, and all intermediate summation values.

An R² of 0.97 means that approximately 97% of the variance in the Y (dependent) variable is explained by the X (independent) variable in the regression model. This indicates a very strong linear relationship between the two variables.

No — R² is a metric used to evaluate a linear regression model, not the model itself. Linear regression finds the best-fit line through your data, while R² tells you how well that line actually fits. A high R² indicates the regression line closely follows the actual data points.