This correlation calculator finds the Pearson correlation coefficient (r) between two paired data sets — how strongly they move together — plus r² and the least-squares regression line. Enter pairs of numbers below.
What Is Correlation?
The Pearson correlation coefficient, r, measures the strength and direction of the linear relationship between two variables, on a scale from −1 to +1. r = +1 means the points form a perfectly rising line; r = −1 a perfectly falling one; r = 0 means no linear pattern at all. Correlation is the gateway statistic of data analysis — and, together with its sibling Covariance, the raw material of regression. This calculator is part of our Statistics Calculators collection.
Worked Example (Verified)
X: 1, 2, 3, 4, 5 — Y: 2, 4, 5, 4, 5 (the classic textbook pair):
- r = 0.7746 — a strong positive correlation
- r² = 0.60 — about 60% of the variation in Y is linearly accounted for by X
- Regression line: y = 0.6x + 2.2 — each extra X predicts 0.6 more Y
Reading r — the Standard Scale
| |r| range | Interpretation |
|---|---|
| 0.90 – 1.00 | Very strong |
| 0.70 – 0.89 | Strong |
| 0.50 – 0.69 | Moderate |
| 0.30 – 0.49 | Weak |
| 0.00 – 0.29 | Negligible |
Three Warnings Every User of r Needs
- Correlation is not causation. Ice-cream sales correlate with drowning (both are driven by summer). r measures co-movement, never mechanism.
- r only sees straight lines. A perfect U-shaped relationship can score r ≈ 0. Always plot before concluding "no relationship."
- Outliers can manufacture or destroy r. One distant point can drag a cloud's r from 0.2 to 0.8 — the reason the Quartile Calculator's outlier check belongs in the same workflow.
Related Tools
- Covariance Calculator — the unscaled sibling of r
- Standard Deviation Calculator
- Statistics Calculators — the full collection
Frequently Asked Questions
What is a good correlation coefficient?
Context decides. In physics, 0.99 may be expected; in social science, 0.3 can be a meaningful finding. The table above gives the conventional reading, not a grade.
What does r² mean?
The share of one variable's variance linearly explained by the other: r = 0.77 → r² = 0.60, so 60% of Y's variation tracks X (in the linear-model sense).
Can correlation be greater than 1?
No — r is bounded by −1 and +1 by construction (it is a covariance normalized by the two standard deviations, and the Cauchy–Schwarz inequality does the rest).
Does zero correlation mean the variables are unrelated?
No — it means no linear relationship. Curved patterns (U-shapes, circles) can hide inside r = 0. Plot your data.
What is the difference between correlation and covariance?
Covariance keeps the original units and scale; correlation divides it into a unit-free −1…+1 index. Same numerator — correlation is covariance standardized.
Is this correlation calculator free?
Yes — free, instant, no sign-up.