Pearson correlation
Calculate Pearson r for the linear relationship between two numeric variables, similar to Excel CORREL or PEARSON output.
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Correlation Coefficient Calculator: Pearson r, Spearman rho, and P-Value
Paste paired x-y data and calculate Pearson correlation, Spearman rank correlation, covariance, R-squared, p-values, a Pearson confidence interval, ranks, and a scatterplot. Use it to check Excel CORREL, PEARSON, RSQ, SPSS, R, or statistics homework output.
- Pearson r Measure linear association between two numeric variables.
- Spearman rho Measure monotonic association using ranks.
- P-values Check whether the observed association is statistically significant.
- Scatterplot See whether the relationship looks linear, curved, or outlier-driven.
Calculate Pearson and Spearman Correlation
Enter paired values with x first and y second. Each line should represent one observation, so the x and y values must stay matched. Use Pearson r for linear relationships and Spearman rho when the relationship is monotonic, ordinal, or sensitive to outliers.
Put one pair on each line, such as 1, 2.1 or 1 2.1.
The first number is x and the second number is y.
Pearson r is unchanged by this choice. The covariance denominator changes only for the covariance output.
Results
Correlation from paired data
Count
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Pearson r
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Pearson p-value
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95% CI for Pearson r
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Spearman rho
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Spearman p-value
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R-Squared
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Covariance
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Interpretation
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Pearson p-values use the usual t approximation for testing zero linear correlation. Spearman p-values shown here are an approximate large-sample check.
Scatterplot
| X | Y | Rank X | Rank Y |
|---|---|---|---|
| Calculate correlation to view ranks. | |||
What This Calculator Includes
Correlation measures the strength and direction of association between two variables. It does not prove that one variable causes the other.
Spearman correlation
Calculate Spearman rank correlation for monotonic relationships and ordinal-style data.
Inference
Review p-values, R-squared, covariance, and a 95% confidence interval for Pearson r.
Visual check
Use the scatterplot to see whether the association is linear, curved, or outlier-driven.
Correlation Formulas
Pearson correlation uses the original values. Spearman correlation converts each variable to ranks first, then calculates Pearson correlation on the ranks.
| Measure | Formula idea | Use when |
|---|---|---|
| Pearson r | Sxy / sqrt(Sxx * Syy) |
The relationship is reasonably linear and both variables are numeric. |
| Spearman rho | Pearson r of ranks |
The relationship is monotonic, ordinal, or affected by outliers. |
| R-squared | r * r |
You want the share of y variation explained by a simple linear relationship with x. |
| Covariance | Sxy / denominator |
You want joint variation in original units rather than standardized units. |
How to Calculate Correlation Step by Step
Correlation homework usually requires more than the r value. The best answer explains the paired data, method choice, direction, strength, p-value, and graph.
- Keep each x value paired with the correct y value from the same observation.
- Make a scatterplot to check whether the relationship looks linear, monotonic, or outlier-driven.
- Use Pearson r for a roughly linear numeric relationship.
- Use Spearman rho when the data are ranks or the relationship is monotonic but not clearly linear.
- Report the correlation coefficient, sample size, p-value if required, and R-squared when relevant.
- Interpret direction and strength in context, and do not claim causation from correlation alone.
Correlation Examples
These examples are useful for checking Excel, SPSS, R, and calculator output. P-values are rounded because software packages may display different decimal places.
| Question type | Data pattern | Result | Interpretation |
|---|---|---|---|
| Pearson correlation | Default paired x-y example | r = 0.9969, p approximately 7.57e-8 | Very strong positive linear association. |
| R-squared | Same paired x-y example | R-squared = 0.9938 | About 99.38% of y variation is explained by a linear relationship with x. |
| Spearman correlation | Same paired x-y example | rho = 1.0000 | The ranks move perfectly upward together in this example. |
Common Mistakes to Avoid
- Treating correlation as proof that one variable causes the other.
- Using Pearson correlation when the scatterplot is strongly curved or driven by outliers.
- Ignoring paired-data order. Each x value must match the y value from the same observation.
- Reporting only r without explaining direction, strength, sample size, p-value, and context.
Correlation Calculator FAQs
What is the difference between Pearson and Spearman correlation?
Pearson correlation measures linear association using the original values. Spearman correlation measures monotonic association by applying Pearson correlation to the ranked values.
Does correlation mean causation?
No. Correlation describes association between variables, but it does not prove that one variable causes the other.
When should I use Spearman correlation?
Use Spearman correlation when the relationship is monotonic but not clearly linear, when the data are ranks, or when outliers make Pearson correlation misleading.
Why does the calculator show covariance too?
Covariance shows direction and joint variation in original units. Correlation standardizes covariance so the result is unitless and always between -1 and 1.
Is this like Excel CORREL or PEARSON?
Yes. Pearson r follows the same correlation idea used by Excel CORREL and PEARSON for paired numeric data. Small differences can appear from rounding.
What does R-squared mean in correlation?
For simple linear association, R-squared is r squared. It is often interpreted as the proportion of variation in y explained by a linear relationship with x.
What should I report for a correlation assignment?
Report the sample size, Pearson r or Spearman rho, direction, strength, p-value if required, graph/outlier notes, and a context-based interpretation.
Need Help Explaining Correlation Output?
Correlation assignments often need a graph, method choice, p-value, strength and direction statement, outlier discussion, and a warning that correlation does not prove causation.
Related Statistics Help
Use Calculators Responsibly
Use this calculator to check computations, compare software output, and prepare tutoring questions. For graded work, follow your course rules and explain the results in context.