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Correlation Coefficient Calculator

Paste paired data to measure how strongly two variables move together. You get Pearson's r, Spearman's rank correlation, r², significance tests and a plain-English interpretation.

Data format

x, y pairsTwo lists

x, y pairs (one pair per line)

e.g. 1, 2.1 — commas, spaces or tabs. Paste two spreadsheet columns directly.

X values

Separated by commas, spaces or new lines

Y values

Enter your values to see the result.

How to use the Correlation Coefficient Calculator

Paste your data as x, y pairs or as two separate lists.
Press Calculate: results also update as you type.
Read Pearson r for a straight-line relationship and Spearman ρ for any monotonic one.
Check the p-value to see whether the correlation is statistically significant.
Look at the scatter plot for curves or outliers that a single number can hide.

Correlation formulas

Pearson's r: r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² · Σ(y − ȳ)²)

Spearman's ρ: rank each variable (ties get the average rank) and apply Pearson's formula to the ranks. With no ties this equals ρ = 1 − 6Σd² / (n(n² − 1)), where d is the difference between the two ranks of each pair.

Significance: t = r √((n − 2) / (1 − r²)) with n − 2 degrees of freedom.

Example: x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5 give Σ(x − x̄)(y − ȳ) = 6, Σ(x − x̄)² = 10 and Σ(y − ȳ)² = 6, so r = 6 / √60 ≈ 0.775.

Interpreting the coefficient

\|r\| or \|ρ\|	Strength	Example reading for r = +value
0.00 – 0.19	Very weak	Essentially no relationship
0.20 – 0.39	Weak	A slight tendency for y to rise with x
0.40 – 0.59	Moderate	A clear but loose upward trend
0.60 – 0.79	Strong	y usually rises when x rises
0.80 – 1.00	Very strong	Points lie close to a rising line or curve

Negative values read the same way, with y tending to fall as x rises. Want the line itself? Use the linear regression calculator.

Frequently asked questions

What is a correlation coefficient?

A correlation coefficient is a number from −1 to 1 that measures how strongly two variables are related. 1 is a perfect positive relationship, −1 a perfect negative one and 0 means no linear (or monotonic) relationship.

What is the difference between Pearson and Spearman correlation?

Pearson's r measures a straight-line relationship using the raw values. Spearman's ρ is Pearson's r computed on the ranks, so it measures any consistently increasing or decreasing (monotonic) relationship and is less affected by outliers.

How is Pearson's r calculated?

r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² × Σ(y − ȳ)²). It is the covariance of x and y divided by the product of their standard deviations.

What counts as a strong correlation?

A common rule of thumb: |r| below 0.2 is very weak, 0.2–0.4 weak, 0.4–0.6 moderate, 0.6–0.8 strong and 0.8–1 very strong. Conventions vary by field.

How do I know if a correlation is significant?

The calculator tests whether r differs from zero using t = r√((n − 2)/(1 − r²)) with n − 2 degrees of freedom. A two-tailed p-value below 0.05 is usually called significant.

Does correlation mean causation?

No. Two variables can be correlated because of coincidence, a third factor that drives both, or reverse causation. Correlation shows association, not cause and effect.

How are tied values handled in Spearman's correlation?

Tied values receive the average of the ranks they would occupy, and ρ is computed as Pearson's r on those ranks. The shortcut 1 − 6Σd²/(n(n² − 1)) is exact only when there are no ties.

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