Correlation Coefficient Calculator
Calculate correlation coefficient (Pearson r and Spearman ρ) between two datasets. Find the strength and direction of relationships with R², scatter plots, regression lines, and step-by-step calculations.
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Correlation Coefficient Calculator - Pearson & Spearman
Calculate correlation coefficients to measure the relationship between two variables. Compute Pearson r for linear relationships, Spearman ρ for monotonic relationships, and coefficient of determination (R²). Includes interactive scatter plots with regression lines and detailed statistical analysis.
What is the Correlation Coefficient?
The correlation coefficient is a statistical measure that describes the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, where +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear relationship. Pearson's r measures linear correlation, while Spearman's ρ measures monotonic relationships and is more robust to outliers.
Pearson Correlation Formula
r = Σ(xᵢ - x̄)(yᵢ - ȳ) / √[Σ(xᵢ - x̄)² × Σ(yᵢ - ȳ)²]How to Use This Calculator
Correlation Analysis Applications
Scientific Research
Measure relationships between variables in experiments, from drug dosage effects to environmental factors.
Financial Analysis
Assess portfolio diversification by measuring correlation between asset returns, currencies, or economic indicators.
Marketing Analytics
Analyze relationships between advertising spend and sales, customer satisfaction and retention rates.
Educational Assessment
Study correlations between study hours and test scores, attendance and academic performance.
Frequently Asked Questions
Use Pearson (r) when your data is continuous, normally distributed, and you expect a linear relationship. Use Spearman (ρ) when data is ordinal, has outliers, is non-normal, or when you're testing for any monotonic relationship (not just linear). Spearman is also better for ranked data or when relationships are curved but consistently increasing or decreasing.