What is the difference between atan and atan2 in C++?

std::atan2 allows calculating the arctangent of all four quadrants. std::atan only allows calculating from quadrants 1 and 4.

Another thing to mention is that atan2 is more stable when computing tangents using an expression like atan(y / x) and x is 0 or close to 0.

atan(x) Returns the principal value of the arc tangent of x, expressed in radians.

atan2(y,x) Returns the principal value of the arc tangent of y/x, expressed in radians.

Notice that because of the sign ambiguity, a function cannot determine with certainty in which quadrant the angle falls only by its tangent value (atan alone). You can use atan2 if you need to determine the quadrant.

Consider a right angled triangle. We label the hypotenuse r, the horizontal side y and the vertical side x. The angle of interest α is the angle between x and r.

C++ atan2(y, x) will give us the value of angle α in radians. atan is used if we only know or are interested in y/x not y and x individually. So if p = y/x then to get α we'd use atan(p).

You cannot use atan2 to determine the quadrant, you can use atan2 only if you already know which quadrant your in! In particular positive x and y imply the first quadrant, positive y and negative x, the second and so on. atan or atan2 themselves simply return a positive or a negative number, nothing more.

With atan2 you can determine the quadrant as stated here.

You can use atan2 if you need to determine the quadrant.

In atan2, the output is: -pi < atan2(y,x) <pi
and in atan, the output is: -pi/2 < atan(y/x) < pi/2 //it dose NOT consider the quarter.
If you want to get the orientation between 0 and 2*pi (like the high-school math), we need to use the atan2 and for negative values add the 2*pi to get the final result between 0 and 2*pi.
Here is the Java source code to explain it clearly:

System.out.println(Math.atan2(1,1)); //pi/4 in the 1st quarter
System.out.println(Math.atan2(1,-1)); //(pi/4)+(pi/2)=3*(pi/4) in the 2nd quarter

System.out.println(Math.atan2(-1,-1 ));//-3*(pi/4) and it is less than 0.
System.out.println(Math.atan2(-1,-1)+2*Math.PI); //5(pi/4) in the 3rd quarter

System.out.println(Math.atan2(-1,1 ));//-pi/4 and it is less than 0.
System.out.println(Math.atan2(-1,1)+2*Math.PI); //7*(pi/4) in the 4th quarter

System.out.println(Math.atan(1 ));//pi/4
System.out.println(Math.atan(-1 ));//-pi/4