Two Variable PCA Calculator
Calculate two-variable principal-component variances and loadings from paired observations.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Center the two variables and diagonalize either their sample covariance or standardized correlation matrix.
Eigenvalues=(Sxx+Syy)/2 ± √(((Sxx−Syy)/2)²+Sxy²)
Worked example
For Y=2X exactly, the second component variance is zero and the first component explains all variance.
Assumptions and input details
Paired complete observations; raw variables must use meaningful scales, and both must vary for standardized PCA. Component signs are conventional. Isotropic data have no unique principal axis; no significance test, causal factor or prediction model is inferred.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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