Tip: This online Pearson correlation calculator accepts negative values and decimals.
What is Pearson correlation?
Pearson correlation is a statistical measure that tells you how strongly two numeric variables move together in a linear way. It is represented by r, and ranges from -1 to +1.
- r = +1: perfect positive linear relationship
- r = 0: no linear relationship
- r = -1: perfect negative linear relationship
If you are comparing things like study time vs exam score, ad spend vs revenue, or sleep hours vs reaction time, a Pearson correlation online calculator is one of the fastest ways to quantify the relationship.
How to use this Pearson correlation online calculator
Step-by-step
- Enter all X values in the first box.
- Enter the matching Y values in the second box.
- Make sure both lists have the same number of data points.
- Click Calculate Pearson r.
The tool returns the correlation coefficient, coefficient of determination (r²), means, standard deviations, and a plain-language interpretation.
Pearson correlation formula
The calculator uses the standard formula based on centered values:
r = Σ[(xᵢ - x̄)(yᵢ - ȳ)] / √(Σ(xᵢ - x̄)² · Σ(yᵢ - ȳ)²)
This version is numerically stable and commonly used in statistics software.
How to interpret your result
Direction
- Positive r: as X increases, Y tends to increase.
- Negative r: as X increases, Y tends to decrease.
Strength (rule-of-thumb)
- 0.00 to 0.09: negligible
- 0.10 to 0.29: weak
- 0.30 to 0.49: moderate
- 0.50 to 0.69: strong
- 0.70 to 1.00: very strong
These cutoffs are guidelines, not universal laws. The context of your field (finance, health, education, engineering) matters.
When should you use Pearson correlation?
Pearson is a good choice when:
- Both variables are numeric and continuous.
- The relationship is approximately linear.
- Outliers are limited or already handled.
- Data are paired observations from the same cases.
If your data are ordinal, strongly non-linear, or heavily skewed with outliers, Spearman rank correlation may be more appropriate.
Common mistakes to avoid
- Mixing unmatched pairs: each X must match the correct Y.
- Assuming causation: correlation does not prove one variable causes the other.
- Ignoring outliers: one extreme point can change r dramatically.
- Using tiny samples: very small n can produce unstable estimates.
- Using Pearson for curved patterns: non-linear trends can produce misleadingly low r.
Quick practical example
Suppose you want to test if weekly practice hours (X) are related to test performance (Y). You enter both lists and get r = 0.78. That indicates a very strong positive linear relationship. The calculator also shows r² = 0.6084, meaning about 60.84% of score variation is linearly associated with practice hours.
FAQ
Can this calculator handle decimals and negative numbers?
Yes. It accepts integers, decimals, and negative values.
Do both arrays need the same length?
Yes. Pearson correlation requires one-to-one paired observations.
What does r² mean?
r² is the coefficient of determination. It shows the proportion of variance in Y that is linearly associated with X.
Does a high correlation mean causation?
No. Correlation measures association, not cause-and-effect.