🔗 Correlation Coefficient Calculator
Calculate Pearson’s correlation coefficient for two paired numeric variables.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate Pearson’s correlation coefficient for two paired numeric variables.
| Concept | Formula or rule |
|---|---|
| Correlation Coefficient Calculator | r = Σ[(x−x̄)(y−ȳ)] / √[Σ(x−x̄)²Σ(y−ȳ)²] |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: Pearson r measures the strength and direction of a linear relationship.
✓ r ranges from −1 to +1
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Claiming causation
Correlation alone does not establish cause.
Correlation alone does not establish cause.
⚠️
Ignoring nonlinear patterns
A strong curved relationship can have low Pearson r.
A strong curved relationship can have low Pearson r.
⚠️
Using unpaired lists
Each X must match the Y at the same position.
Each X must match the Y at the same position.
Practice Questions
1. What is the range of r?
Answer: −1 to +1
2. Does r=0 prove independence?
Answer: No.
3. Does correlation imply causation?
Answer: No.
Frequently Asked Questions
What does r=1 mean?▾
A perfect positive linear relationship.
What does r=0 mean?▾
No linear association, though nonlinear association may exist.
Is correlation affected by units?▾
No, Pearson r is unitless.