R-squared (R²) is one of the most-cited numbers in statistics, but it's also one of the most misunderstood. This calculator computes R² two ways — from raw paired data via a least-squares fit, and directly from a correlation coefficient — so you can see exactly why the two methods always agree, and what the resulting number does and doesn't tell you.
How the R-Squared Calculator works
When you enter paired X and Y values, the calculator fits the least-squares regression line — the line that minimizes the sum of squared vertical distances (residuals) between each point and the line. It then computes R² = 1 − SSres/SStot, comparing the leftover error after fitting the line (SSres) to the total variability in Y before any model was applied (SStot).
When you enter a correlation coefficient r instead, the calculator uses the algebraic identity R² = r², which holds exactly for simple linear regression with one predictor. Both paths land on the same number for the same underlying data — that equivalence is the core idea this calculator is built to demonstrate.
Inputs and what they mean
On the R² tab, X and Y should be paired lists of the same length — each position in X corresponds to the same position in Y. Mismatched or non-numeric entries are skipped in pairs so a single typo doesn't silently shift every value after it out of alignment.
On the From Correlation tab, r must be a decimal between −1 and 1. This is the standard range for a Pearson correlation coefficient; values outside that range are not valid correlations and the calculator will flag them.
Limits and edge cases
R² only measures how well a linear model fits — a strong curved (nonlinear) relationship can produce a low R² even when X and Y are tightly related, so always look at the scatter plot alongside the number. R² also tends to increase automatically as more predictors are added to a model (not a concern for this single-variable calculator, but worth knowing if you move to multiple regression, where adjusted R² is the more honest comparison).
A high R² does not by itself prove causation, and a handful of outliers can inflate or deflate R² substantially. Treat R² as one diagnostic among several, not a final verdict on a model's usefulness.