About this calculator
Enter paired data, such as study hours and marks. The calculator also tests whether the correlation is significant and gives Spearman’s rank correlation.
How to use it
- Enter the X values.
- Enter the matching Y values in the same order.
- Read r, r² and the p-value.
The formula
r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² × Σ(y − ȳ)²); t = r√(n − 2) ÷ √(1 − r²)
- r
- Karl Pearson’s coefficient
- n
- number of pairs
Worked example
Hours 2, 4, 5, 7, 9, 10, 12 and marks 11, 15, 16, 22, 24, 23, 30
- r = 0.978, a very strong positive correlation.
- p = 0.00014, so it is significant at 5%.
What the result means
Strength: above 0.7 is strong, 0.3 to 0.7 moderate, below 0.3 weak. Always look at a scatter plot too.
Assumptions
- Paired data; Pearson assumes a straight-line relationship.
Limitations
- Correlation does not prove cause and effect.
Frequently asked questions
What is a good correlation?
It depends on the field, but |r| above 0.7 is usually called strong.
When should I use Spearman?
When the data are ranks, have outliers or the relationship is curved but steadily rising or falling.
What does r² mean?
The share of the variation in one variable that goes with the other.
Last reviewed on 6 October 2026. Found a mistake? Tell us.