RESEARCH STATISTICS GUIDE
Pearson r interpretation table: how strong is your correlation?
Pearson's r runs from −1 to +1. Its sign gives the direction of the relationship and its size gives the strength. Use the table below to put a verbal label on r, then check the p value before you call the relationship significant.Explore research statistics & data analysis →FORMULA OR CORE IDEA
r = Σ(x − x̄)(y − ȳ) ÷ √[Σ(x − x̄)² × Σ(y − ȳ)²], df = n − 2WORKED EXAMPLE
15 students' study hours and exam scores give r = .79, p < .001. The relationship is positive, very strong by the table below, and statistically significant; r² = .63 means hours explain about 63% of the variation in scores.QUICK REFERENCE
Pearson r interpretation table
Use the absolute value of r. SolveGrid's calculators use the labels in the middle column; Cohen's (1988) small / medium / large benchmarks are shown for comparison.| Absolute value of r | Strength | Cohen (1988) |
|---|---|---|
| .00 – .09 | Negligible | — |
| .10 – .29 | Weak | Small (≈ .10) |
| .30 – .49 | Moderate | Medium (≈ .30) |
| .50 – .69 | Strong | Large (≥ .50) |
| .70 – 1.00 | Very strong | Large |
STEP BY STEP
Read the direction from the sign
A positive r means both variables rise together. A negative r means one rises as the other falls. The sign says nothing about strength: r = −.60 is as strong as r = +.60.
Read the strength from the size
Ignore the sign and match the absolute value of r to the strength table. State which table you used, because thesis panels and fields differ.
Check statistical significance
Test r with t = r√(n − 2) ÷ √(1 − r²) on n − 2 degrees of freedom. If p < .05 the correlation is statistically significant. A strong r in a tiny sample can still be non-significant.
Report shared variance
Square r to get r², the share of variation the two variables have in common. r = .50 means only 25% shared variance, which is why moderate correlations are often less impressive than they sound.
Avoid causal wording
Write “is related to” or “is associated with”, not “causes” or “affects”. Correlation alone does not show which variable influences the other, or whether a third variable drives both.
Write it up
“There was a very strong, positive, statistically significant correlation between study hours and exam scores, r(13) = .79, p < .001.” Drop the leading zero for r and p in APA style.
COMMON QUESTIONS
Frequently asked questions
What is a strong Pearson correlation?
Values of .50 or more (positive or negative) are usually called strong, and .70 or more very strong. By Cohen's benchmarks, .10 is small, .30 medium and .50 large.
Is r = 0.4 a strong correlation?
It is usually described as moderate. It means about 16% shared variance (0.4² = .16). Whether that matters depends on your field: in social science research, .40 can be a meaningful relationship.
What does a negative correlation mean?
As one variable increases, the other tends to decrease, for example more absences and lower grades. A negative r of −.65 is just as strong as +.65.
Can a correlation be strong but not significant?
Yes. With very few participants, even a large r can have p > .05 because the estimate is uncertain. Report both the size of r and its p value.
Should I use Pearson or Spearman?
Use Pearson for two numeric variables with a roughly linear relationship and no extreme outliers. Use Spearman's rho for ranks, single Likert items, or clearly skewed data. The same strength table works for both.