R² (coefficient of determination) measures the proportion of variance in the observed data explained by the model. An R² of 0.85 means the model explains 85% of the variability in the dependent variable.

What is a good R² value?

It depends on the field. In physics or engineering, R² above 0.99 is common. In social sciences, 0.50–0.70 may be acceptable. Context and domain norms matter more than any single threshold.

Yes. A negative R² means your model performs worse than a simple horizontal mean line. This usually indicates a fundamentally wrong model or data entry errors.

What is the difference between R and R²?

R is the Pearson correlation coefficient (–1 to 1) measuring linear relationship strength. R² is its square, always 0–1, and represents the proportion of variance explained by the model.

Does this calculator do linear regression?

No. You supply both observed and predicted values. If you need predicted values from raw X-Y data, enter X as predicted and Y as observed and click "Fit simple linear regression" — the tool will estimate the best-fit line first.

Root Mean Squared Error (RMSE) is the square root of the average squared difference between observed and predicted values. It is expressed in the same units as your data, making it easy to interpret alongside R².

R-Squared Calculator

Name: R-Squared Calculator
Availability: InStock
Author: Nham Vu

Enter your observed and predicted (or X and Y) values to instantly calculate R², SS_res, SS_tot, and RMSE.

Data Input

Observed (Y) Predicted (Ŷ)

Enter your data on the left and click Calculate R²

Coefficient of Determination

—

R²

0 — No fit 1 — Perfect fit

SS_res (Residual)

—

Sum of squared residuals

SS_tot (Total)

—

Total sum of squares

RMSE

—

Root mean squared error

n (Pairs)

—

Number of data points

Residuals Table

#	Observed	Predicted	Residual	Residual²

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Summary

Enter your observed and predicted (or X and Y) values to instantly calculate R², SS_res, SS_tot, and RMSE.

How it works

Enter your observed (actual) values in the left column, one per line.
Enter your predicted (model output) values in the right column, one per line.
Click Calculate to get R², SS_res, SS_tot, and RMSE.
R² ranges from 0 to 1; values closer to 1 indicate a better model fit.
Use the sample data button to see an example before entering your own numbers.

Use cases

Evaluate how well a linear regression model fits your data.
Compare two regression models to pick the better predictor.
Assess forecast accuracy in finance and sales projections.
Validate machine learning model predictions against ground truth.
Grade the fit of a trend line drawn through a scatter plot.
Report goodness-of-fit in academic research or data science projects.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu