ToolBark
Math

Correlation Coefficient Calculator

Find the Pearson r between any two variables instantly

Enter Paired Data

Separate values with commas, spaces, or new lines. X and Y must have the same number of values.

Results

Pearson r0.9931
PositiveVery Strong

The two variables move almost perfectly together.

Pearson r0.9931
R² (coefficient of determination)0.9863
DirectionPositive
StrengthVery Strong
N (number of pairs)10
Mean X9.6
Mean Y9.6
Std Dev X5.0636
Std Dev Y4.22374
Covariance (population)21.24

Data pairs (10)

#XY(x−x̄)(y−ȳ)
12350.16
24525.76
35616.56
4784.16
5890.96
6109-0.24
712113.36
8141314.96
9161534.56
10181762.16

How it works

Pearson r
Measures the strength and direction of a linear relationship between two variables. Ranges from −1 (perfect negative) to +1 (perfect positive).
R² (r-squared)
The proportion of variance in Y explained by X. An R² of 0.81 means X explains 81% of Y's variation.
Positive correlation
As X increases, Y tends to increase. r close to +1.
Negative correlation
As X increases, Y tends to decrease. r close to −1.
Strength thresholds
|r| ≥ 0.9 very strong · ≥ 0.7 strong · ≥ 0.5 moderate · ≥ 0.3 weak · < 0.3 negligible.
Covariance
Raw measure of how X and Y vary together (population formula). Pearson r normalizes this by the product of standard deviations.
About

A correlation coefficient calculator computes the Pearson r — the standard measure of linear association between two variables. Paste your paired X and Y values, separated by commas or new lines, and get the correlation coefficient, R², direction, and strength interpretation in one click. Useful for statistics homework, data analysis, and research validation.

FAQ
What does the Pearson r value mean?+

Pearson r ranges from −1 to +1. A value of +1 means a perfect positive linear relationship (as X rises, Y rises proportionally), −1 means a perfect negative relationship, and 0 means no linear association. Values around ±0.7 or higher are generally considered strong.

How many data points do I need?+

You need at least 3 paired data points to compute a meaningful correlation. In practice, 10 or more pairs give a more reliable result, since small samples can produce misleadingly high r values by chance.

What is the difference between r and R²?+

r (Pearson r) measures the strength and direction of the linear relationship. R² (r-squared) is simply r multiplied by itself and represents the proportion of variance in Y that is explained by X. For example, r = 0.9 gives R² = 0.81, meaning X explains 81% of the variation in Y.

Does a high correlation mean causation?+

No. Correlation only measures the degree to which two variables move together linearly. A high r value does not prove that changes in X cause changes in Y — a third variable (confound) or coincidence could explain the relationship.

Related tools