📊 Correlation Calculator
Calculate Pearson's correlation coefficient to measure the strength and direction of linear relationships between two variables.
Enter pairs of numbers separated by spaces or commas. Each line represents one data point (x, y).
Correlation Coefficient (r)
0.9922
Very strong linear relationship.
X Variable Statistics
- Mean: 3.0000
- Std Dev: 1.5811
Y Variable Statistics
- Mean: 6.8000
- Std Dev: 3.3466
Covariance: 5.2500
Data Points: 5
How to Use This Calculator
Enter paired data
Input your x and y values, one pair per line. Separate values with spaces or commas (e.g., "1 3" or "1, 3").
Review correlation coefficient
The calculator displays Pearson's r, which ranges from -1 to +1. Values closer to ±1 indicate stronger linear relationships.
Interpret the results
Positive r means variables increase together. Negative r means one increases as the other decreases. r near 0 suggests no linear relationship.
Check additional statistics
Review means, standard deviations, and covariance to better understand your data and the relationship between variables.
Formula
r = Cov(X, Y) / (σₓ × σᵧ)
Where r is the correlation coefficient, Cov(X, Y) is the covariance, and σₓ and σᵧ are the standard deviations of X and Y.
Covariance Formula
Cov(X, Y) = Σ[(xᵢ - x̄)(yᵢ - ȳ)] / (n - 1)
Example
For data pairs (1,3), (2,4), (3,7), (4,9), (5,11): r ≈ 0.997, indicating a very strong positive linear relationship.
Full Description
The correlation coefficient (Pearson's r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
This calculator computes Pearson's correlation coefficient using the standard formula based on covariance and standard deviations. It also provides descriptive statistics (means, standard deviations) to help you understand your data better.
Interpreting Correlation Values
- |r| > 0.8: Very strong linear relationship
- 0.6 < |r| ≤ 0.8: Strong linear relationship
- 0.4 < |r| ≤ 0.6: Moderate linear relationship
- 0.2 < |r| ≤ 0.4: Weak linear relationship
- |r| ≤ 0.2: Very weak or no linear relationship
Ideal for
- ✅ Statistical analysis and research
- ✅ Data science and machine learning
- ✅ Quality control and process analysis
- ✅ Academic studies and homework
- ✅ Understanding relationships in datasets
Frequently Asked Questions
What does a correlation of 0 mean?
A correlation of 0 means there is no linear relationship between the variables. However, they might still have a nonlinear relationship that correlation cannot detect.
Does correlation imply causation?
No. Correlation measures association, not causation. Two variables can be correlated without one causing the other. There may be a third variable influencing both, or the relationship may be coincidental.
What's the difference between correlation and regression?
Correlation measures the strength of a linear relationship. Regression finds the equation of the line that best fits the data and can be used for prediction.
Can I use this for non-linear relationships?
Pearson's correlation measures linear relationships. For non-linear relationships, consider Spearman's rank correlation or other non-parametric methods.
How many data points do I need?
You need at least 2 pairs, but more data points provide more reliable results. For meaningful analysis, aim for at least 10-20 data points.
What if my correlation is negative?
A negative correlation means that as one variable increases, the other decreases. The strength is indicated by the absolute value. For example, r = -0.9 indicates a very strong negative relationship.