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Free correlation coefficient calculator to measure linear relationship strength between paired variables. Enter X and Y values to compute Pearson r, R-squared, direction, and interpretation in real time.
Last updated: April 20, 2026
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Pearson r
0.8528
R²
0.7273
Direction
Positive
Strength
Strong
Sample size
5
Interpretation
The paired data shows a strong positive linear relationship.
Formula
r = Σ[(x - x̄)(y - ȳ)] / √(Σ(x - x̄)² Σ(y - ȳ)²)
Use with care:
Range
-1.0000 to +1.0000
Interpretation
Explained variance proportion
Output
Direction + strength labels
X: [1, 2, 3, 4, 5], Y: [2, 4, 5, 4, 6]
Correlation (r)
0.8528
R²
0.7273
The calculator computes Pearson correlation by centering X and Y around their means, then normalizing covariance by the product of standard deviations. This produces a scale-free linear association metric between -1 and +1.
r = Σ[(x - x̄)(y - ȳ)] / √(Σ(x - x̄)² Σ(y - ȳ)²)The closer |r| is to 1, the stronger the linear relationship. Values near 0 indicate weak or no linear trend.
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