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Correlation Calculator
Calculate the Pearson correlation coefficient between two data series.
Pearson Correlation
Industry-standard linear correlation measure
R-Squared
See how much variance is explained
Instant Interpretation
Strength and direction labelled automatically
Calculate Correlation
Enter two data series (comma or newline separated) to find the Pearson correlation coefficient.
How the Pearson Correlation Coefficient Works
The Formula
r = Σ((xi-x̄)(yi-ȳ)) / √(Σ(xi-x̄)² × Σ(yi-ȳ)²)
The formula measures how much X and Y deviate from their means together. When both tend to be above or below their means simultaneously, r is positive. When one is above while the other is below, r is negative.
Interpretation Scale
r = +1: perfect positive (both move up together). r = -1: perfect negative (one goes up, other goes down). r = 0: no linear relationship (could still have a non-linear one). R² tells you the percentage of variance in Y explained by X — an r of 0.7 means R² = 0.49, so about 49% of the variation is explained.
Correlation in Portfolio Management
Positive Correlation
Assets that move together (e.g., tech stocks with similar business models) provide little diversification benefit. A portfolio concentrated in highly correlated assets amplifies risk — when one falls, they all tend to fall. Typical correlation between major equity indices: 0.7-0.9.
Low/Negative Correlation
Combining assets with low or negative correlation reduces portfolio volatility without necessarily reducing expected returns — the "free lunch" of diversification. Stocks and government bonds historically have low or negative correlation. Gold and equities also tend to have low correlation.
How to Use This Correlation Calculator
Enter Data
Paste two series of equal length, comma or newline separated.
Calculate
Click calculate to compute the Pearson r and R².
Interpret
Review strength, direction, and variance explained.
Correlation Does Not Imply Causation
- Spurious correlations. Ice cream sales and drowning deaths are correlated — both are caused by summer heat, not each other. Always consider confounding variables before inferring cause and effect.
- Regime changes. Correlations measured during calm markets may not hold during crises. During the 2008 financial crisis, previously uncorrelated assets became highly correlated as investors sold everything.
- Non-linear relationships. Pearson correlation only captures linear relationships. Two variables could have a strong curved relationship but show r ≈ 0. Consider scatter plots and other measures for non-linear patterns.
- Sample size matters. Small datasets can produce misleading correlations. With only 5 data points, even r = 0.8 may not be statistically significant. More data points give more reliable results.
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