calculate r squared

What does “calculate R squared” mean?

When people ask how to calculate R squared, they’re usually talking about the coefficient of determination, written as R². It tells you how much variation in an outcome (Y) is explained by a predictor or model (X).

In plain language: if R² is 0.64, then about 64% of the variability in your dependent variable is explained by your model. The remaining 36% is due to other factors, randomness, measurement noise, or model misspecification.

Quick formula: if you already know r

If you have Pearson’s correlation coefficient r, then computing R² is simple:

R² = r²

• If r = 0.90, then R² = 0.81 (81%).
• If r = -0.60, then R² = 0.36 (36%).

Notice that a negative correlation still produces a positive R². That’s because squaring removes the sign and focuses only on explained variation.

How to calculate R² from raw data

Step 1: Collect paired observations

You need matched values for each observation, like (hours studied, exam score) or (ad spend, revenue). In the calculator above, place those in X and Y fields with equal lengths.

Step 2: Fit a linear relationship

A simple linear regression estimates a line: Y = a + bX, where b is slope and a is intercept.

Step 3: Compute explained vs total variation

A common regression definition is: R² = 1 - (SSE / SST)

• SSE: Sum of squared errors (unexplained variation)
• SST: Total sum of squares (total variation in Y)

The closer SSE is to zero, the closer R² gets to 1.

How to interpret R² correctly

R² is useful, but context matters:

• High R² can indicate strong fit, but doesn’t prove causation.
• Low R² can still be valuable in noisy fields (behavior, finance, medicine).
• Always pair R² with residual analysis, domain knowledge, and validation checks.

R² vs Adjusted R²

Regular R² never decreases when you add more predictors, even if they are useless. Adjusted R² corrects for model complexity and is better for comparing models with different numbers of features.

If you’re building multiple regression models, adjusted R² is often the better “apples-to-apples” metric.

Common mistakes when calculating R squared

• Using mismatched X and Y list lengths.
• Interpreting R² as “accuracy” for every modeling task.
• Assuming high R² means the model will generalize to new data.
• Ignoring non-linear relationships that linear R² may miss.
• Confusing correlation with causation.

Practical takeaway

To calculate R², square r when correlation is available—or compute it from regression sums of squares from raw data. Use the calculator above for both workflows. Then interpret the result in context, not in isolation.