Correlation Calculator
Enter two sets of numbers to calculate Pearson r correlation coefficient. Includes scatter plot and interpretation.
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Calculator results are estimates based on your inputs. They are useful for learning, planning, and comparison, but they are not professional advice.
Use responsibly
Use the result as a practical first pass, then verify any important decision with the appropriate source or professional.
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What correlation helps you answer
Correlation helps you test whether two numeric variables move together. Analysts use it to check whether ad spend and leads rise together, whether study time and exam scores are associated, or whether two operational metrics are connected strongly enough to investigate further. It is a screening tool for relationships, not proof of cause.
Pearson correlation coefficient formula
r = Σ((x-x̄)(y-ȳ)) / √(Σ(x-x̄)² × Σ(y-ȳ)²)
Where x̄ and ȳ are the means of the X and Y datasets.
Interpreting r values
- r = 1.0 means perfect positive linear correlation.
- r = 0.7 to 0.9 is usually considered strong.
- r = 0.4 to 0.6 is moderate.
- r = 0.1 to 0.3 is weak.
- r = 0 means no linear correlation.
- Negative values mean the variables move in opposite directions.
What r squared adds
r squared, also called the coefficient of determination, estimates how much of the variation in Y is explained by the linear relationship with X. If r = 0.8, then r² = 0.64, which suggests 64% of the variance is explained by the linear relationship. That sounds precise, but it still does not tell you whether the relationship is causal or useful in a business decision.
Real-world examples
- Marketing: compare spend and conversions to see whether channels move together.
- Research: test whether study time is associated with score or outcome.
- Operations: check whether temperature, demand, staffing, or response times move with another KPI.
Important limitations
Pearson correlation only measures linear relationships. A curved or threshold-based relationship can still produce a low r. Outliers can also create or destroy apparent correlation. Always inspect the data, and remember the basic rule: correlation is not causation.
Related tools and guides
- Standard Deviation Calculator to understand spread before interpreting relationships.
- Outlier Detector if extreme values may be distorting the correlation.
- Sample Size Calculator when you are planning a study before collecting data.