How to calculate the angle of a vector from the vertical?

Do not take the absolute value of the arguments to atan2. The whole point of atan2 is that it uses the signs of its arguments to work out which qaudrant the angle is in. By taking the absolute values you are forcing atan2 to only return values between 0 and pi/2 instead of -pi to pi.

You first have to understand how to compute angle between two vectors and there are several of them. I will give you what I think is the simplest.

1. Given v1 and v2, their dot product is: v1x * v2x + v1y * v2y
2. The norm of a vector v is given by: sqtr(vx^2+vy^2)

With this information, please take this definition:

dot(v1, v2) = norm(v1) * norm(v2) * cos(angle(v1, v2))

Now, you solve for angle(v1, v2):

angle(v1, v2) = acos( dot(v1, v2) / (norm(v1) * norm(v2)) )

Finally, taking the definitions given at the beginning, then you end up with:

angle(v1, v2) = acos( (v1x * v2x + v1y * v2y) / (sqrt(v1x^2+v1y^2) * sqrt(v2x^2+v2y^2)) )

Again, there are many ways to do this, but I like this one because it is helpful for dot product given angle and norm, or angle, given vectors.

The answer will be in radians, but you know that pi radians (that is 3.14 radians) are 180 degrees, so you simply multiply by the conversion factor 180/pi.

Aha! Turns out I just needed to flip my angle and use atan2. This is my final code:

private float calcAngle(float x, float y, float x1, float y1)
{
    float _angle = (float)Math.toDegrees(Math.atan2(x1-x, y-y1));
    return _angle;
}

Thanks everyone for helping me figure this out and also for helping me to understand what I'm actually doing! :)