Statistics Calculator: Correlation Coefficient

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

Correlation Coefficient Calculator


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 xi,yi couple on separate lines:


  • All xi values in the first line and all yi values in the second line:


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:

$ r ={\frac{n \sum_{i=1}^n x_i y_i - \sum_{i=1}^n x_i \sum_{i=1}^n y_i}{\sqrt {(n \sum_{i=1}^n x_i^2 - (\sum_{i=1}^n x_i)^2)(n \sum_{i=1}^n y_i^2 - (\sum_{i=1}^n y_i)^2)} } $

where n is the total number of samples, xi (x1, x2, ..., xn) are the x values and yi are the y values.

Another Calc

how to make an improper fraction into a whole number how to convert a mixed number to an improper fraction finding the gcf of two numbers mm to in converter calculator metric length conversions convert centigrade to celsius who invented the temperature scale how many cm to an inch calculator m2 square feet convert short ton to kg how to work out iqr how many centigrams in a kilogram milligrams to kilograms chart lcm maths definition centimeter to millimeter calculator 2.5 grams to milligrams meters to square feet conversion inches centimeters conversion symbol for picometer lcm calculator that shows work 2.5 pounds in grams mixed percent to fraction calculator compute fractions calculator change mixed number to improper fraction calculator how do you do percents on a calculator square feet to square meter calculation farenheit to degree celcius online graphing calculator scatter plot conversion square feet to square meters what is 225 mm in inches convert degree celcius to kelvin convert a mixed number to a fraction