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Pearson Correlation Calculator — result sheet
Calculate Pearson’s r, r², means, and supporting sums from paired X and Y observations entered as comma-separated values.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] ÷ √(Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²); r² is the squared coefficient.
Pearson’s r summarizes the direction and strength of a linear association in paired numeric observations. The result is accompanied by means and r² so the calculation remains inspectable.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Enter 2–30 finite numbers separated by commas or spaces.
- Y values — Enter the same number of paired values as X.
Worked example
| Input | Value |
|---|---|
| X values | 1, 2, 3, 4, 5 |
| Y values | 2, 4, 5, 4, 7 |
The paired data have r ≈ 0.870 and r² ≈ 0.758.
Assumptions and limits
- X and Y contain the same number of finite numeric observations.
- At least three paired observations are entered.
- Neither variable is constant; otherwise Pearson’s r is undefined.
- The observations are paired in order, so xᵢ and yᵢ describe the same row or case.
- The coefficient describes linear association and does not prove causation.
- Outliers, missingness, measurement error, and sampling design are not automatically diagnosed.
- Interpretation should include the study context, a scatter plot, and appropriate uncertainty analysis.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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