The Arctangent is the inverse of the tangent.
Therefore, for the simple rightangled triangle below, the arctangent of the opposite side, o, divided by the adjacent side, a, is equal to the angle θ.
i.e. for the triangle above,
The Inverse trig. functions are discussed further on the Wikipedia Inverse Trigonometric Functions Page
The Excel ATAN2 function calculates the arctangent (ie. the inverse tangent) of a given set of x and y coordinates, and returns an angle, in radians, between π/2 and +π/2.
The format of the function is :
Where the x_num and y_num arguments are the x and y coordinates of the point that you want to calculate the arctangent of.
Note: the angle returned from the Atan2 function may be positive, representing a counterclockwise angle from the xaxis, or negative, representing a clockwise angle from the xaxis. This result is given in radians.
Converting from Radians to Degrees
If you want the angle returned by the Atan2 function to be expressed in degrees, you can convert it, using the Excel Degrees function:
Column A of the spreadsheet below, shows examples of the Excel Atan2 Function, used to calculate the arctangent of different x and y coordinates. In the example in cell A4, the result is converted from radians, into degrees.
The formulas are shown in the spreadsheet on the left and the results are shown in the spreadsheet on the right.
Formulas:

Results:

Further information and examples of the Excel Atan2 function can be found on the Microsoft Office website.
If you get an error from the Excel Atan2 Function, this is likely to be one of the following:
#DIV/0!    Occurs if the supplied x_num and y_num arguments are both equal to 0 
#VALUE!    Occurs if either of the supplied arguments are nonnumeric 