Pearson Correlation Calculator
Enter paired observations to measure linear association using Pearson's r.
Pearson r
0.9922
Mean X / Std X
μx = 3.0000 • sx = 1.5811
Mean Y / Std Y
μy = 6.8000 • sy = 3.3466
Pairs: 5
Interpretation: Very strong linear relationship.
Instructions
- Enter paired (x, y) observations, one pair per line.
- Ensure the data show variability (no constant series).
- Review Pearson's r and supporting statistics.
- Use the correlation to assess strength and direction of linear association.
Formula
r = Σ[(xi − μx)(yi − μy)] / √[Σ(xi − μx)² Σ(yi − μy)²]
μx, μy = sample means; Σ covers all paired observations
Pearson correlation ranges from −1 (perfect negative) to +1 (perfect positive). Values near zero indicate weak linear relationships.
About This Tool
Pearson's r quantifies linear association between two continuous variables. Use it to detect trends, validate regression assumptions, or compare experiment outcomes. Because it depends on mean and standard deviation, Pearson's r is sensitive to outliers and non-linear patterns.
Common Questions
What if one variable has zero variance?
Correlation is undefined; this calculator returns 0 and advises using datasets with variation.
Does Pearson correlation detect non-linear relationships?
No. Pearson's r only measures linear relationships. Consider Spearman or Kendall coefficients for monotonic but non-linear relationships.
Can I use this for categorical data?
No. Pearson correlation is meant for continuous numeric data.
Should I remove outliers first?
Outliers can heavily influence Pearson's r. Inspect data visually and consider robust alternatives if needed.