What this result means
Calculate R squared from observed and predicted values with SSE, SST and negative-result support.
Coefficient of Determination Calculator
Use the Coefficient of Determination Calculator to calculate and interpret r squared.
Coefficient of Determination
Enter your values, then calculate to see a verified result.
Reference range
How this result is calculated
A clear calculation path based on your inputs.
Inputs usedReview the information used for this result.
Full calculation and sourcesR² = 1 - SSE / SST. Negative values are not clamped.
Versioned calculationFormula v1.0.0
Method used
R² = 1 - SSE / SST. Negative values are not clamped.
Important limitation
The result is only as reliable as the inputs and stated method.
Enter the inputsUse values with the units and definitions shown beside each field.
Apply the methodR² = 1 - SSE / SST. Negative values are not clamped.
Inspect the bridgeReview the primary result and supporting outputs before using it.
Check limitationsConfirm the assumptions, date, jurisdiction or population match your use case.
Interpretation
The calculator compares squared prediction errors with variance around the observed mean.
R² = 1 - SSE / SST. Negative values are not clamped.
The result is only as reliable as the inputs and stated method.
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Report a calculation issue Coefficient of Determination Calculator: purpose and method
Calculates r squared, SSE, SST, and pairs from observed values and predicted values with visible method, validation, precision, and limitations.
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Method and test recordFormula v1.0.0
- Recorded scope
- Coefficient of Determination Calculator formula, input validation, edge behavior and result presentation.
- Publisher
- CalculatorGeek
- Reviewed by
- CalculatorGeek Editorial Team
- Recorded review date
- 2026-09-21
- Next source review
- 2027-09-21
- Definition fixtures
- 1 configured scenarios
- Published examples
- 1 shown below
Recorded method
Package reconciliation, primary-source mapping, competitor feature comparison, deterministic fixtures, PHP/JavaScript parity and responsive preview QA.
These records describe the published model and reference tests. A test-case count is not a certification of every possible input or an independent specialist review. Editorial policy
Known limitations
- The result is only as reliable as the inputs and stated method.
- Changing legal, medical, exam or statistical conventions must be checked at the source.
Method sources
Latest model update
2026-09-21 -
Reference inputs and expected results
Up to 12 examples from the configured definition fixtures are shown. Expected values use the stated output units; invalid inputs are intended to be rejected.
| Case | Inputs | Expected result |
|---|---|---|
| Primary worked example | Observed values: 3, 5, 7, 9; Predicted values: 2.5, 5.5, 6.5, 9.5 | R squared: 0.95; SSE: 1; SST: 20; Pairs: 4 (allowed numeric tolerance: 0.0001) |
Report an issue with this tool. Include the page URL, units, expected answer, and steps to reproduce. Do not include sensitive personal information.
On this page
Direct answer
Calculate R squared from observed and predicted values with SSE, SST and negative-result support.
Continue with the Covariance Calculator when that method matches your next question.
Continue with the Descriptive Statistics Calculator when that method matches your next question.
Formula and methodology
R² = 1 - SSE / SST. Negative values are not clamped.
The calculator compares squared prediction errors with variance around the observed mean.
Worked example
The calculator compares squared prediction errors with variance around the observed mean.
The calculator retains working precision and rounds only the displayed values.
Interpret the result carefully
Method boundary: The result is only as reliable as the inputs and stated method.
Inputs, boundary behavior and JavaScript/PHP parity are covered by deterministic release tests.
Use the result for the named task only. Do not stretch it into a legal, clinical, safety or causal conclusion the formula does not support.
Inputs, outputs and result meaning
Calculates r squared, SSE, SST, and pairs from observed values and predicted values with visible method, validation, precision, and limitations.
Inputs
- Observed values
- Enter observed Y values.
- Predicted values
- Enter model predictions in matching order.
Outputs
- R squared
- This is the primary result. The visible value uses up to 6 decimal places according to the output rule.
- SSE
- The visible value uses up to 6 decimal places according to the output rule.
- SST
- The visible value uses up to 6 decimal places according to the output rule.
- Pairs
- The visible value is displayed without decimal places.
The calculator applies the documented method after validating and normalizing the inputs. Keep the result label, unit, selected mode, and stated limitations together when sharing the answer.
Frequently asked questions
What method does this calculator use?
R² = 1 - SSE / SST. Negative values are not clamped.
How should I round the result?
Keep full precision during the calculation and round only the final display unless a governing standard says otherwise.
What is the main limitation?
The result is only as reliable as the inputs and stated method.
Can I reproduce the answer?
Yes. The formula, inputs, supporting outputs and worked example are displayed on the page.
Sources
Source research refreshed September 21, 2026. No rankings, review credentials or official affiliation are implied.