Correlation Coefficient Calculator - Mathematical Calculations & Solutions
Separate values with commas
Must match number of X values
How It Works
Input Data Pairs
Enter X and Y values separated by commas
Calculate Pearson r
Apply statistical correlation formula
Common Examples
Correlation Coefficient Calculator
What
Measure the strength and direction of linear relationships between two variables.
Why
Essential for data analysis, research, statistics, and understanding variable relationships.
Applications
Statistics, research, finance, psychology, economics, and scientific studies.
Calculation Table
| Correlation Range | Strength | Example | Interpretation |
|---|---|---|---|
| ±0.90 to ±1.00 | Very Strong | r = +0.95 | Almost perfect linear relationship |
| ±0.70 to ±0.89 | Strong | r = -0.82 | Strong linear relationship |
| ±0.50 to ±0.69 | Moderate | r = +0.65 | Moderate linear relationship |
| ±0.30 to ±0.49 | Weak | r = -0.35 | Weak linear relationship |
| 0.00 to ±0.29 | Very Weak | r = 0.15 | Little to no linear relationship |
Frequently Asked Questions
What is a correlation coefficient?
A correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 to +1.
How do I input my data?
Enter X values in the first box and Y values in the second box, separated by commas. Both datasets must have the same number of values.
What does r = 0.8 mean?
An r value of 0.8 indicates a strong positive correlation, meaning as one variable increases, the other tends to increase proportionally.
What's the difference between positive and negative correlation?
Positive correlation: both variables move in the same direction. Negative correlation: variables move in opposite directions.
Does correlation prove causation?
No! Correlation only shows association. High correlation doesn't mean one variable causes changes in the other - there could be other factors involved.
What if my correlation is close to zero?
A correlation near zero (e.g., -0.1 to +0.1) suggests little to no linear relationship between the variables, though non-linear relationships may still exist.
Can I use this for any type of data?
This calculator works best with continuous numerical data. For categorical or ordinal data, other correlation methods like Spearman's rank correlation may be more appropriate.