R Squared Calculator
Enter paired X and Y values and this tool returns the coefficient of determination (R squared) along with the Pearson correlation r for the two lists. R squared tells you what share of the variation in Y is explained by X.
What this calculator does
The R Squared Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Enter paired X and Y values and this tool returns the coefficient of determination (R squared) along with the Pearson correlation r for the two lists. R squared tells you what share of the variation in Y is explained by X. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About R Squared Calculator
This calculator takes two comma-separated lists of numbers and computes the coefficient of determination (R²) together with the underlying Pearson correlation r. R² is simply r squared, so it always lands between 0 and 1 and describes how much of the variation in your Y values moves with X.
Reach for it when you have paired measurements and want a quick read on how tightly they track each other before committing to a full regression report.
Formula & Mathematical Calculation
Calculation Method
- Compute } den=Math.sqrt((n × sx2-sx × sx) × (n × sy2-sy × sy))
- Compute } r=(n × sxy-sx × sy) ÷ den
Calculation Example
Enter X values of 1, 2, 3, 4 and Y values of 2, 4, 5, 8, then click Calculate.
The tool returns R² = 0.9627 and Correlation r = 0.9812, with the note: “R² = 0.9627, meaning 96.27% of the variance in Y is explained by X.”
Key Benefits
- Reports both R squared and the Pearson correlation r from a single pair of lists
- Accepts free-form comma-separated input and ignores stray separators when parsing numbers
- Adds a plain-language interpretation stating the percentage of Y's variance explained by X
- Flags lists that are unequal in length, shorter than two points, or have no variation instead of returning a misleading value
How to Use this Calculator
-
Enter your X values
Type the independent values into the X field, separated by commas, for example 1, 2, 3, 4. -
Enter matching Y values
Type the same number of dependent values into the Y field, for example 2, 4, 5, 8. -
Calculate
Click Calculate to display the R squared box and the Correlation r box. -
Read the result
Check the R squared value and the interpretation line, which converts it to the percent of Y's variance explained by X.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- R Squared Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.