Statistics
R-Squared Calculator
Enter paired data and mathcheck fits the least-squares line, then reports R² as the share of the variation in y that the line explains, with SSR, SSE, and SST shown.
Already have r? Switch modes to square it and get adjusted R² for your sample size and number of predictors.
1 for a simple x-y regression. Adjusted R² penalizes extra predictors.
Try an example
Result
R²
—
- Adjusted R²
- —
- Correlation r
- —
- Variation explained
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- Fitted line
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- SSR (explained)
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- SSE (residual)
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More details (1 more)
- SST (total)
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Study path
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What the r-squared calculator solves
Enter paired data and mathcheck fits the least-squares line, then reports R² as the share of the variation in y that the line explains, with SSR, SSE, and SST shown. Already have r? Switch modes to square it and get adjusted R² for your A smaller group taken from a population, used to estimate facts about the whole group. size and number of predictors.
Formula
How to use it
- Paste x and y lists of equal length (at least 3 pairs), or switch to 'from r' and enter the correlation The number multiplying a variable, like the 3 in 3x. with the sample size.
- Set the number of predictors (1 for a straight-line fit) so adjusted R² is computed correctly.
- Read R² as a share of explained variation and compare it with adjusted R².
- Open 'Show the work' to see SST, SSE, SSR, and the fitted line.
How to read the answer
R² ranges from 0 to 1. R² = 0.81 means 81% of the variation in y is accounted for by the linear relationship with x; the remaining 19% is residual scatter. Adjusted R² is slightly smaller and stops rising when you add predictors that do not help. High R² does not prove causation and does not mean the line predicts individual points closely if SSE is large in absolute terms.
Common mistakes and edge cases
- Reading R² as the How steep a line is: how much y changes for each step right in x. or as a probability; it is a proportion of variance.
- Comparing R² between models with different numbers of predictors without using adjusted R².
- Assuming a low R² means no relationship; a curved relationship can have a low linear R².
- Identical y values give SST = 0, so R² is undefined rather than 1.
Worked examples
Nearly linear data
R²
0.9982
Scattered data
R²
0.8115
From r = 0.85 with n = 30
R²
0.7225
Negative r gives the same R²
R²
0.36
No relationship
R²
0.2
Undefined: constant y
R²
Error
Frequently asked questions
What does R² mean?+
The coefficient of determination is the fraction of the variation in y that a regression model explains. R² = 0.64 means 64% explained, 36% left in the residuals.
Is R² just r squared?+
For a simple regression with one predictor, yes: R² equals the square of the Pearson correlation. With several predictors R² is computed from the sums of squares instead.
What is adjusted R² and when should I use it?+
Adjusted R² penalizes extra predictors: 1 - (1 - R²)(n - 1)/(n - k - 1). Use it to compare models with different numbers of predictors; it can even be negative for a useless model.
What is a good R² value?+
It depends on the field. Physics experiments often exceed 0.95; social science surveys may treat 0.3 as meaningful. Judge R² together with the residual pattern and sample size.
Can R² be negative?+
Not for a least-squares line with an intercept, where it lies between 0 and 1. Adjusted R² and R² for a model without an intercept can go negative.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026