# Correlation Coefficient Calculator

URL: https://speedycalculator.com/calculators/statistics/correlation-coefficient/
Last updated: 2026-10-25

> The correlation calculator finds Pearson’s correlation coefficient r between two lists of numbers, plus R², the regression slope and intercept. Enter X and Y values in the same order.

## Inputs

- X values
- Y values

## Results

- Pearson r
- R²
- Slope
- Intercept

## Formula

```
r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² Σ(y − ȳ)²)
```

## Explanation

Correlation measures the strength of a linear relationship from −1 (perfect negative) to +1 (perfect positive).

### How to use the Correlation Coefficient Calculator

- **X values**
- **Y values**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The covariance of X and Y is divided by the product of their standard deviations.

### Inputs explained

FieldWhat to enterX valuesA list of numbers separated by commas, spaces or new linesY valuesA list of numbers separated by commas, spaces or new lines

### What each result means

- **Pearson r** = corr([X values], [Y values])
- **R²** = [Pearson r]^2
- **Slope** = slope([X values], [Y values])
- **Intercept** = intercept([X values], [Y values])

## Worked example

Inputs — X values: 1, 2, 3, 4, 5, 6; Y values: 2.1, 3.9, 6.2, 7.8, 10.1, 12.2.

Results — **Pearson r = 0.9991**; R² = 0.99821; Slope = 2.02; Intercept = -0.02.

## FAQ

**Does correlation mean causation?**
No; a third factor or coincidence can create correlation.

**What does R² mean?**
The share of variance in Y explained by a straight-line relationship with X.

**What formula does the Correlation Coefficient Calculator use?**
r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² Σ(y − ȳ)²).


## Sources

- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)