Pearson Correlation Coefficient Calculator
Enter two equal-length numeric datasets (X and Y). You can separate values with commas, spaces, or new lines.
Tip: the 1st X value pairs with the 1st Y value, the 2nd with the 2nd, and so on.
What this correlation coefficient online calculator does
This tool computes the Pearson correlation coefficient (r), a value between -1 and +1 that measures the strength and direction of a linear relationship between two variables.
- r = +1: perfect positive linear relationship
- r = -1: perfect negative linear relationship
- r = 0: no linear relationship
It also reports R² (coefficient of determination), means, and sample covariance so you can quickly interpret your dataset.
How to use it
Step 1: Enter your data
Put your first dataset in the X box and your second dataset in the Y box. Both lists must contain the same number of values.
Step 2: Click calculate
The calculator instantly computes the correlation and shows a plain-English interpretation of the relationship.
Step 3: Interpret responsibly
Correlation measures association, not cause-and-effect. A high correlation does not prove that one variable causes the other.
Pearson correlation formula
The calculator uses this formula:
Where x̄ and ȳ are the means of X and Y. This formula compares how both variables move around their averages.
Interpreting correlation strength
Common rough guidelines for |r| are:
- 0.00 to 0.19: very weak
- 0.20 to 0.39: weak
- 0.40 to 0.59: moderate
- 0.60 to 0.79: strong
- 0.80 to 1.00: very strong
Sign indicates direction: positive means both tend to increase together; negative means one tends to decrease as the other increases.
Common mistakes to avoid
- Using unequal list lengths (pairs must align).
- Including non-numeric characters in your data.
- Interpreting correlation as proof of causation.
- Ignoring outliers, which can strongly change r.
- Using Pearson correlation for clearly non-linear relationships.
When to use Pearson vs. Spearman
Pearson (this calculator)
Use when your variables are numeric and the relationship is approximately linear.
Spearman
Use when your data are ranked, not normally distributed, or the pattern is monotonic but not linear.
Quick FAQ
Can I use decimals and negative values?
Yes. The calculator accepts integers, decimals, and negative numbers.
What does a negative correlation mean?
It means as one variable goes up, the other tends to go down.
What is a “good” correlation?
It depends on the field. In social sciences, moderate correlations may be meaningful; in engineering, stronger values may be expected.
Why did I get an error saying correlation is undefined?
If all X values or all Y values are identical, there is no variation in one variable, so Pearson correlation cannot be computed.