If we have a vector finding the magnitude is easy. The formular we need is tan()=. We can rewrite this formular so we get the angle: =arctan(). You may find the arc tangent on your calcuator as tan. If the vector is parallel to one axis, we can determine the angle by looking at the parallel axis and the direction it is pointing: Parallel to x-axis: Points to the right -> 0° Points to the left -> 180° Parallel to the y-axis: Points upwards -> 90° Points downwards -> 270° In the other cases we need to calculate the angle and take a look in which direction the vector points. Upper right: we can take the angle as we got it from our formular Down right: we need to add +360° to our angle. left: we need to add +180° to our angle. For Example: we get -54 degrees for our angle and it points to the left we calculate: -54°+180°= 126° Exercise: Move the slider and watch how the angle is calculated. If you know the solution, you can check it everytime.