# Statistics Calculator: Correlation Coefficient

**Use this calculator to calculate the correlation coefficient from a set of bivariate data. **

## Correlation Coefficient Calculator

### Instructions

This calculator can be used to calculate the **sample correlation coefficient**.

Enter the x,y values in the box above. You may enter data in one of the following two formats:

- Each x
_{i},y_{i}couple on separate lines:

x_{1},y_{1}

x_{2},y_{2}

x_{3},y_{3}

x_{4},y_{4}

x_{5},y_{5}

- All x
_{i}values in the first line and all y_{i}values in the second line:

x_{1},x_{2},x_{3},x_{4},x_{5}

y_{1},y_{2},y_{3},y_{4},y_{5}

Press the "Submit Data" button to perform the calculation. The correlation coefficient will be displayed if the calculation is successful. To clear the calculator and enter new data, press "Reset".

### What is the correlation coefficient

The **correlation coefficient**, or **Pearson product-moment correlation coefficient (PMCC)** is a numerical value between -1 and 1 that expresses the **strength of the linear relationship between two variables**.When r is closer to 1 it indicates a strong positive relationship. A value of 0 indicates that there is no relationship. Values close to -1 signal a strong negative relationship between the two variables. You may use the linear regression calculator to visualize this relationship on a graph.

### Correlation coefficient formula

There are many formulas to calculate the correlation coefficient (all yielding the same result). This calculator uses the following:

where

*n*is the total number of samples,

*x*are the x values and y

_{i}(x_{1}, x_{2}, ..., x_{n})_{i}are the y values.