Correlation Coefficient Calculator
Calculate Pearson’s and Spearman’s correlation with scatter plot visualization
About Correlation Coefficient
A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. The most commonly used correlation coefficients are Pearson’s r and Spearman’s ρ.
Pearson's r measures the linear relationship between two continuous variables. The coefficient value ranges from -1 to 1:
- +1 indicates a perfect positive linear correlation
- 0 indicates no linear correlation
- -1 indicates a perfect negative linear correlation
Spearman's ρ measures the strength and direction of the monotonic relationship between two ranked variables. It's particularly useful when:
- Data is not normally distributed
- There are outliers that might skew Pearson's results
- You're dealing with ordinal or ranked data
This tool not only gives final correlation values but also displays a step-by-step breakdown of each calculation. It's ideal for:
- Students learning statistics
- Teachers demonstrating concepts
- Analysts verifying their computations
The steps show how the values are derived — enhancing understanding and transparency.
How to Use
- Enter two sets of numeric values (X and Y) of equal length.
- Separate values with commas or spaces.
- Alternatively, upload a CSV file with two columns of numbers.
- Results and scatter plot update automatically.
- Use the Download CSV button to save data and results.
- A step-by-step breakdown of the correlation calculations is displayed below the results, showing intermediate values and formulas used.
Frequently Asked Questions
Pearson measures the strength of a linear relationship between two continuous variables, while Spearman measures the strength of a monotonic relationship using the ranks of values. Pearson is sensitive to outliers; Spearman is more robust for non-linear or ordinal data.
Use Spearman correlation when your data is not normally distributed, contains outliers, or involves ordinal/ranked variables. It's also preferred when the relationship is monotonic but not necessarily linear.
A correlation of 0 means there is no linear relationship between the variables. However, a non-linear relationship may still exist.
No. Correlation only shows that two variables are related in some way — it does not imply that one causes the other. For causation, further statistical analysis or controlled experiments are required.
Both Pearson's and Spearman's correlation coefficients range from -1 to +1. A value of +1 means a perfect positive correlation, -1 means perfect negative, and 0 means no correlation.