If we have a vector [math]\text{\vec{a}}[/math] finding the magnitude is easy.[br]The formular we need is tan([math]\text{\alpha}[/math])=[math]\frac{y}{x}[/math].[br]We can rewrite this formular so we get the angle: [math]\text{\alpha}[/math]=arctan([math]\frac{y}{x}[/math]).[br]You may find the arc tangent on your calcuator as tan[math]^{^{-1}}[/math].[br][br]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:[br][br]Parallel to x-axis:[br]Points to the right -> 0°[br]Points to the left -> 180°[br][br]Parallel to the y-axis:[br]Points upwards -> 90°[br]Points downwards -> 270°[br][br]In the other cases we need to calculate the angle [math]\text{\alpha}[/math] and take a look in which direction the vector points. [br]Upper right: we can take the angle as we got it from our formular[br]Down right: we need to add +360° to our angle.[br]left: we need to add +180° to our angle.[br][br]For Example: we get -54 degrees for our angle and it points to the left we calculate: -54°+180°= 126°[br][br]Exercise: Move the slider and watch how the angle is calculated. If you know the solution, you can check it everytime.