The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables, for example study hours and exam scores. This calculator gives r, r², the t statistic, a two-tailed p-value, the 95% confidence interval (Fisher z), the regression line, a scatter plot and a ready APA 7 sentence.
How to use this calculator
- Put variable X in one column and variable Y in the next; each row is one participant.
- Copy both columns (headers optional) and paste them.
- Click Calculate and check the scatter plot for a straight-line pattern and outliers.
- Copy the APA sentence.
Formula
r = Σ(x − x̄)(y − ȳ) / √[Σ(x − x̄)² · Σ(y − ȳ)²] t = r · √(n − 2) / √(1 − r²), df = n − 2 95% CI: tanh(atanh(r) ± 1.96 / √(n − 3))
Step-by-step example
- Ten students’ study hours (X) and exam scores (Y).
- r = 0.994, so r² = 0.989 (about 99% of the variance in scores is shared with study hours).
- t(8) = 26.73, p < .001.
- 95% CI [.98, 1.00].
How to interpret the results
| |r| | Strength (Cohen, 1988) |
|---|---|
| < .10 | Negligible |
| .10 – .29 | Small / weak |
| .30 – .49 | Medium / moderate |
| ≥ .50 | Large / strong |
A positive r means both variables rise together; a negative r means one rises as the other falls. A significant p-value means the correlation is unlikely to be zero in the population. Correlation does not imply causation.
How to report it in APA 7 style
A Pearson correlation showed a strong, positive and statistically significant relationship between study hours and exam scores, r(8) = .99, p < .001, 95% CI [.98, 1.00].
Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.
Assumptions
- Both variables are continuous.
- The relationship is linear (check the scatter plot).
- Both variables are approximately normally distributed (bivariate normality).
- No influential outliers.
- Observations are independent.
How to do it in SPSS, R or Excel
SPSS: Analyze → Correlate → Bivariate → Pearson. R: cor.test(x, y). Excel: =CORREL(x, y) (r only, no p-value).
Roman Urdu mein khulasa
Pearson correlation batata hai ke do variables (jaise parhai ke ghante aur marks) aapas mein kitne jure hue hain. r +1 ke qareeb ho to strong positive rishta hai, −1 ke qareeb ho to strong negative. p 0.05 se kam ho to correlation significant hai. Yaad rakhein ke correlation ka matlab ye nahi ke aik variable dusre ki wajah hai.
Frequently asked questions
What is a strong correlation?
By Cohen’s (1988) guidelines, |r| of .10 is small, .30 medium and .50 or more large. In many social science fields, r above .50 is considered strong.
When should I use Spearman instead of Pearson?
Use Spearman’s rank correlation when the data are ordinal (such as single Likert items), clearly non-normal, or the relationship is monotonic but not linear.
What does r² mean?
r² (the coefficient of determination) is the proportion of variance the two variables share. For example, r = .60 gives r² = .36, meaning 36% shared variance.
Can I correlate Likert scale totals?
Yes. Total or mean scores from multi-item Likert scales are usually treated as continuous, so Pearson is appropriate. For single Likert items, Spearman is safer.
Does a significant correlation prove causation?
No. Correlation only shows that two variables move together. A third variable or reverse causation could explain the relationship.
How many pairs do I need?
The calculator needs at least 4 pairs, but you need far more for a precise estimate; around 85 pairs gives 80% power to detect a medium correlation (r = .30).
Related calculators
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- Not sure which test to use? Try the test chooser
Cite this calculator
If ScholarCalc helped your analysis, you can cite it in APA 7 format:
ScholarCalc. (2026). Pearson Correlation Calculator [Web application]. https://scholarcalc.com/pearson-correlation-calculator/
Written and maintained by the ScholarCalc team. Last reviewed: November 2026.
Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.