The correlation coefficient is a way to determine the strength of the linear association between two variables, such as "X" and "Y." The correlation will always be between the numbers "1" and "1." If the correlation is negative, then there is a negative relationship. If the correlation is "0," then there is a neutral relationship. If the correlation is positive, then there is a positive relationship.

Write out the numbers of the "X" and "Y" values you want the correlation coefficient of:
X Values Y Values
20 4.1
21 4.6

Count the total number of "X" and "Y" values; in this case, there are four, so "N"=4.

Multiply "X" by "Y," "X" by "X" and "Y" by "Y" for all four values with a calculator:
XY=204.1=82 XY=214.6=96.6
XX=2020=400 XX=2121=441
YY=4.14.1=16.81 YY=4.64.6=21.16

Add up the "X" values, the "Y" values and all of the multiplied "X" and "Y" values; find the square roots of the "X" and "Y" values and add them together:
X+X=20+21=41
Y+Y=4.1+4.6=8.7
XY=204.1=82 and XY=214.6=96.6 and 82+96.6=178.6
XX=2020=400 and XX=2121=441 and 400+441=841
YY=4.14.1=16.81 and YY=4.64.6=21.16 and 16.81+21.16=37.97

Plug the numbers into the formula (r) =[ NΣXY  (ΣX)(ΣY) / Sqrt([NΣX^2  (ΣX)^2][NΣY^2  (ΣY)^2])] and make the calculations with the calculator:
Correlation(r)=((4)(178.6)(41)(8.7)) / squareroot ([4)(841)(4141)][(4)(37.97)(8.7*8.7)])
Correlation(r)=(714.4356.7) / squareroot ([33641681)*[151.8875.69)
Correlation(r)=357.7 / squareroot (1683*76.19)
Correlation(r)=357.7 / squareroot (128227.77)
Correlation(r)=357.7 / 358.089
Correlation(r)=0.9989
Tips & Warnings
 Use a square root calculator, such as Math.com's, to get the square roots of large numbers; simply enter the number and press "Calculate," and the square root will appear.
 Remember to plug the numbers you get from the calculator into their correct places within the formula; you won't get the proper correlation coefficient otherwise, and any number you get that is either below 1 or above 1 is an incorrect coefficient.