Pearson Correlation Calculator
Pair two return series from matching periods and inspect their co-movement.
Paired returns (%) · Pearson linear correlation · not causation
Results
Review or adjust your inputs, then calculate to see your results and interpretation.
Understand this calculation
Pearson r ranges from −1 to +1 and measures the direction and strength of a linear relationship. Positive means same-direction movement, negative means opposite direction. Near zero indicates a weak linear relationship only. It is undefined if either series has no variation.
See calculation method and assumptions
Formula
Pearson Correlation
Divide paired deviation products by the square root of the product of squared-deviation sums. The result is undefined if either sum is zero.
Variables, rates and periods
- xᵢ / yᵢ
- Observations from the same period. A return input of 2 means 2%, calculated directly in percentage units.
- n / x̄ / s
- n is sample size, x̄ the sample mean, and s the sample SD using n−1 in the variance denominator.
- r
- Pearson r measures linear association from −1 to +1, without units. It is undefined if either series has no variation.
Check pairing and shape first
- Use matching periods and frequency across both series.
- Keep complete X/Y pairs.
- Missing values and mismatched counts are reported rather than silently deleting one side.
- Interpret r alongside outliers and nonlinear shapes.
Compare linear co-movement in paired asset returns with Pearson correlation and a scatter plot.
Worked example
- Place X and Y returns from the same period on the same row; 2 means 2%.
- Preserve one-to-one period pairing and check equal counts with no missing values.
- Calculate r and inspect the scatter plot for shape, outliers and nonlinear patterns.
Frequently asked questions
Can I sort the two series separately?
No. Each row represents the same period. Separate sorting or deleting a missing value on only one side breaks pairing and changes the question the correlation answers.
Does r near zero mean no relationship?
No. It indicates weak linear association, while a strong curved relationship may remain. Inspect the scatter plot too.
Does correlation establish causation or a future relationship?
No. Shared factors may drive both series, and historical correlation can change as market conditions change.