Pearson Correlation Coefficient

r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].

Inputs

Result

Loading calculator…
—

General calculation reads

Amazon affiliate
How Not to Be Wrong
Jordan Ellenberg - math thinking
Shop on Amazon
The Joy of X
Steven Strogatz - accessible math
Shop on Amazon
Scientific calculator (Casio fx-991EX)
Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

  • Enter paired x and y values, comma-separated.
  • Calculator pairs them in order.
  • Read r, r², and regression line.

About this calculator

Pearson r measures linear correlation between two variables: r = +1 (perfect positive), 0 (none), −1 (perfect negative). r² = "coefficient of determination" — fraction of variance in y explained by linear relationship with x. Pearson assumes linear, normally-distributed data. For non-linear or rank-based associations, use Spearman ρ. Correlation does not imply causation — always.

Frequently asked

r vs. r²?+
r is the correlation; r² is "% variance explained". r = 0.7 means r² = 0.49 — only 49% explained even with strong correlation.
Pearson vs. Spearman?+
Pearson: linear relationships, continuous data. Spearman: ranks, monotonic but non-linear. Use Spearman for ordinal data.
Correlation = causation?+
No. Strong correlation might be coincidence, common cause, or reverse causation. Need experiment or causal inference to claim causation.
Outlier impact?+
Pearson is sensitive to outliers — one extreme point can flip r. Always plot data. Spearman is more robust.
Sample size minimum?+
r is unreliable with n < 10. For inference, n ≥ 30 + plot residuals.

Related calculators

P-Value Calculator (z to p)
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.
Confidence Interval Calculator
CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.
Normal Distribution Calculator (PDF + CDF)
Compute probability density and cumulative probability at x for given μ, σ.
Binomial Probability Calculator
P(X = k) = C(n,k) p^k (1−p)^(n−k). Probability of exactly k successes in n trials.
Combinations Calculator C(n, r)
C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.
Permutations Calculator P(n, r)
P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

Combinations Calculator C(n, r)
Calc

C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.

Permutations Calculator P(n, r)
Calc

P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.

P-Value Calculator (z to p)
Calc

Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.

Confidence Interval Calculator
Calc

CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.

Normal Distribution Calculator (PDF + CDF)
Calc

Compute probability density and cumulative probability at x for given μ, σ.

Compound Interest Calculator
Finance

Future value of an investment growing with compound interest plus monthly contributions, with a year-by-year line chart (linear or log scale) of balance vs. cumulative contributions.