Significance included
The t-test on r tells you whether a correlation this strong could easily have come from unrelated data.
Tools / Correlation Calculator
Correlation Calculator
Paste your paired values, one x and y per line, and get Pearson's correlation coefficient with r squared and a significance test.
r = Σ(x − x̄)(y − ȳ) ÷ √( Σ(x − x̄)² × Σ(y − ȳ)² )
Paste paired values to see the result
- 1
Paste paired values
One pair per line, x first then y, separated by a space, comma, or tab. Two spreadsheet columns paste in cleanly.
- 2
Check the pair count
Every line must have exactly two numbers. A row with one missing, or a third column carried over from a spreadsheet, is rejected rather than silently trimmed.
- 3
Read r, r², and p
r is the strength and direction, r² is the share of variance explained, and p says whether it is distinguishable from zero.
Why use this correlation calculator
An r on its own can mislead. Ten points can produce r = 0.6 by luck, so the p-value belongs right next to it.
r squared alongside
r = 0.5 sounds moderate until you see it explains only 25% of the variance.
Paste from a spreadsheet
Two columns copied out of a sheet arrive tab separated, which this parses directly.
What to correlate
Survey score relationships
Does satisfaction move with response time, or with number of contacts?
Marketing and traffic
Check whether spend and signups track each other across weeks.
Coursework and lab data
Standard Pearson r with the significance test in one step.
Pearson correlation
r = Σ(x − x̄)(y − ȳ) ÷ √( Σ(x − x̄)² × Σ(y − ȳ)² )
r runs from −1 to 1. The significance test uses t = r√(n − 2) ÷ √(1 − r²) with n − 2 degrees of freedom.
Reading the strength of r
0.0 to 0.1
Negligible
0.1 to 0.3
Weak
0.3 to 0.5
Moderate
0.5 to 1.0
Strong
Cautions worth keeping in mind
- Correlation is not causation. A third variable driving both is the usual explanation.
- Pearson r only measures straight-line relationships. A clear curve can still produce r near zero.
- One outlier can create or destroy a correlation in a small dataset. Plot the points.
- Correlating aggregates, like weekly totals, often inflates r compared with individual-level data.
Related calculators
Frequently asked questions
How do you calculate a correlation coefficient?
Pearson's r is the covariance of x and y divided by the product of their standard deviations:
r = Σ(x − x̄)(y − ȳ) ÷ √( Σ(x − x̄)² × Σ(y − ȳ)² )
The result runs from −1 (perfect inverse) through 0 (no linear relationship) to 1 (perfect positive).
What is a strong correlation?
As a common rough guide, absolute r below 0.3 is weak, 0.3 to 0.5 is moderate, and above 0.5 is strong.
Those bands are conventions, not rules. In physics 0.9 might be disappointing; in social research 0.4 can be a strong finding.
What does r squared mean?
The share of variance in one variable that is explained by a linear relationship with the other. An r of 0.6 gives r² = 0.36, so 36% of the variation is accounted for and 64% is not.
It is a useful antidote to over-reading a moderate r.
Does correlation prove causation?
No. A correlation is consistent with x causing y, y causing x, both being driven by something else, or coincidence.
Only a controlled experiment or a careful causal design can settle direction.
How many pairs do I need?
Three, because the significance test needs at least one degree of freedom: two points always sit on a line, so r is 1 either way and says nothing about a relationship. Any conclusion from fewer than about 20 pairs is fragile, and the p-value here accounts for sample size directly, so a strong r on few points still shows a weak p-value.
What if my data is not linear?
Pearson r will understate a real relationship that curves. Plot the points first. For monotonic but non-linear data, a rank correlation such as Spearman's is more appropriate.
Can I correlate categorical data?
Not with Pearson's r. Use the chi square calculator for two categorical variables and read Cramer's V as the strength of association.
Is my data stored?
No. Parsing and calculation happen in your browser.
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