Correlation Calculator

Calculate Pearson correlation coefficient (r) and r² from two data sets.

Pearson r

0.7746

R²

0.6000

Interpretation

Pearson r0.7746
R² (explained variance)60.00%
StrengthModerate
DirectionPositive
Data Points5

Use the Correlation Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

This calculator determines the Pearson correlation coefficient (r) and the coefficient of determination (r²) between two sets of data. These metrics help you understand the strength and direction of a linear relationship, which is crucial for analyzing trends like the correlation between 2026 Q1 rainfall and crop yields.

The Pearson correlation coefficient (r) is calculated by dividing the covariance of the two variables by the product of their standard deviations. The coefficient of determination (r²) is simply the square of r, representing the proportion of variance in one variable that can be predicted from the other.

Ensure your data sets are paired correctly; each value in the first set must correspond to a specific value in the second. A common mistake is misinterpreting correlation as causation; a strong correlation doesn't necessarily mean one variable causes the other. Always consider lurking variables.

Example: Analyzing Social Media Engagement vs. Sales for a 2026 Product Launch

  1. 1 Input two data sets representing monthly social media engagement (e.g., average likes + shares) and monthly sales figures (in thousands USD) for a new product launched in January 2026: Data Set 1 (Engagement): [1500, 1800, 2200, 2000, 2500, 2800] Data Set 2 (Sales): [25, 30, 38, 35, 42, 48]
  2. 2 The calculator will compute the Pearson correlation coefficient (r) and the coefficient of determination (r²) based on these inputs.
  3. 3 The calculated Pearson correlation coefficient (r) is approximately 0.98. The coefficient of determination (r²) is approximately 0.96.
  4. 4 An r-value of 0.98 indicates a very strong positive linear relationship between social media engagement and sales. The r² value of 0.96 means that 96% of the variation in sales can be explained by the variation in social media engagement for this product in 2026. This suggests that increasing engagement is highly likely to lead to increased sales.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

What does a correlation of 0.8 mean?
A correlation of 0.8 indicates a strong positive linear relationship. As one variable increases, the other tends to increase proportionally. About 64% (0.8² = r²) of the variance in one variable is explained by the other.
Does correlation imply causation?
No. Correlation only measures the linear association between two variables. A strong correlation could be caused by a third confounding variable, coincidence, or reverse causation. Controlled experiments are needed to establish causation.
What is a strong vs weak correlation?
Generally: 0-0.3 is weak, 0.3-0.7 is moderate, and 0.7-1.0 is strong (same thresholds for negative values). The threshold for "meaningful" depends on the field; in social sciences 0.3 may be notable, while physics expects 0.9+.

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