Correlation Coefficient Calculator
Enter paired X and Y values (commas or spaces) to get Pearson r, r², both means and a plain-language read on how strong the relationship is.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
5 values
5 values
0.774597
Correlation coefficient 0.774597- Interpretation
- Strong positive
- r²
- 0.6
- Pairs (n)
- 5
- Mean x̄
- 3
- Mean ȳ
- 4
- Correlation coefficient (r)
- 0.774597
Show steps
- Data: n = 5 pairs. Mean x̄ = 15 ÷ 5 = 3, mean ȳ = 20 ÷ 5 = 4.
- Sum of deviation products Σ((x − x̄)(y − ȳ)) = 6.
- Squared deviations: Σ(x − x̄)² = 10, Σ(y − ȳ)² = 6.
- Correlation coefficient r = 6 ÷ √(10 × 6) = 0.774597; r² = 0.6.
- |r| = 0.774597 ≥ 0.7 — a strong positive correlation.
How to use the correlation calculator
- 1Enter your X values separated by commas or spaces.
- 2Enter your Y values — the same count, in the same order, so each pair lines up.
- 3Read r, r² and the interpretation; open Show steps to see the formula with your numbers.
Correlation ≠ causation
A high ronly means two variables move together — it doesn’t mean one causes the other. Before drawing conclusions, ask whether a third factor could be driving both.
Frequently asked questions
What does the correlation coefficient tell you?
Pearson r measures the strength and direction of a linear relationship between two variables, on a scale from −1 to +1. Values near +1 mean the variables rise together, values near −1 mean one falls as the other rises, and values near 0 mean there is little linear relationship.
What counts as a strong correlation?
This calculator uses common rules of thumb: |r| ≥ 0.7 is strong, 0.5 to 0.7 is moderate, 0.3 to 0.5 is weak, and below 0.3 is little to none. The cut-offs are conventions, not laws — in physics r = 0.8 may be unimpressive, while in social science it is remarkably strong.
Does correlation mean causation?
No. A high r only says two variables move together — it cannot say one causes the other. A third factor may drive both (ice-cream sales and drownings both rise in summer), or the pairing may be pure coincidence.
What is r squared?
r² (the coefficient of determination) is the share of the variation in one variable that is linearly explained by the other. An r of 0.9 gives r² = 0.81, meaning about 81% of the variation is shared; the remaining 19% is unexplained.