Pearson r Score Calculator
Paste two equal-length sets of numbers to calculate the Pearson correlation coefficient (r), coefficient of determination (r2), and a quick interpretation.
Accepted separators: commas, spaces, or new lines. Both lists must contain the same number of values.
What is an r score?
The r score is usually the Pearson correlation coefficient, a statistic that measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1:
- +1: perfect positive linear relationship
- 0: no linear correlation
- -1: perfect negative linear relationship
If you are comparing things like hours studied vs exam score, sleep vs mood, or ad spend vs revenue, the r score helps you quantify how tightly those values move together.
Formula used by this calculator
This page uses the standard Pearson formula:
r = [nΣxy − (Σx)(Σy)] / √([nΣx² − (Σx)²][nΣy² − (Σy)²])
Where n is sample size, and the Σ terms are sums across the paired data points.
How to use this r score calculator
1) Enter paired values
Each x value must line up with the corresponding y value at the same position. For example, if x is daily study time, y should be the score from the same day or same student.
2) Click “Calculate r Score”
The tool instantly computes:
- r (correlation coefficient)
- r² (variance explained by the linear model)
- Direction (positive/negative)
- Strength label (weak/moderate/strong)
3) Interpret carefully
A high correlation can be useful, but remember the golden rule: correlation does not imply causation. A third factor may explain both variables.
Interpreting the result
There is no universal scale, but this practical guide is common:
- |r| < 0.10 → negligible
- 0.10 to 0.29 → weak
- 0.30 to 0.49 → moderate
- 0.50 to 0.69 → strong
- 0.70 to 1.00 → very strong
The sign (+ or -) tells direction, while magnitude (absolute value) tells strength.
Example use case
Suppose you measure weekly exercise hours and resting heart rate changes. If you get r = -0.78, this suggests a strong negative relationship: as exercise increases, resting heart rate tends to decrease. The corresponding r² = 0.61 implies that about 61% of the variation in one variable is linearly associated with the other in your sample.
Common mistakes to avoid
- Using unmatched sample sizes for x and y.
- Including text or symbols in numeric fields.
- Applying Pearson r to clearly non-linear relationships.
- Ignoring outliers that can dramatically change r.
- Treating high correlation as proof of cause-and-effect.
FAQ
Can I use decimals and negative values?
Yes. The calculator accepts integers, decimals, and negative numbers.
What if r is exactly 0?
That means no linear relationship was detected. A non-linear pattern may still exist.
What does r² mean in plain language?
r² is the proportion of variance explained by a linear relationship. For example, r² = 0.36 means 36% of observed variability is associated with that linear fit.
Final note
Use this r score calculator as a fast exploratory tool for statistics, research, and business analysis. For high-stakes decisions, combine it with visualization, domain knowledge, and significance testing.