# get angle of a line from horizon

I want to know how to get an angle of a line A-B from horizontal axis X. Other questions in SO do that only between two lines. I'm aware I can always draw second line A-C and calculate but I'm wondering if there's a faster method.

EDIT: I'm very sure I'm not doing a premature optimization.

## Answers

You can use atan for that.

```angle = atan((By-Ay)/(Bx-Ax))
```

```    private double Angulo(int x1, int y1, int x2, int y2)
{
double degrees;

// Avoid divide by zero run values.
if (x2 - x1 == 0)
{
if (y2 > y1)
degrees = 90;
else
degrees = 270;
}
else
{
// Calculate angle from offset.
double riseoverrun = (double)(y2 - y1) / (double)(x2 - x1);
double radians = Math.Atan(riseoverrun);
degrees = radians * ((double)180 / Math.PI);

// Handle quadrant specific transformations.
if ((x2 - x1) < 0 || (y2 - y1) < 0)
degrees += 180;
if ((x2 - x1) > 0 && (y2 - y1) < 0)
degrees -= 180;
if (degrees < 0)
degrees += 360;
}
return degrees;
}
```

If

1. The angle is small,
2. you can live with small inaccuracies, and
3. You can use the angle in radians and not degrees,

then there is a fast solution: Under these conditions, you can assume that tan(a) = a = atan(a), and hence just omit the atan() call.

You could also use arccosine, if your line is in the form [r_x,r_y], where r_x is the change in x and r_y is the change in y.

```angle = arccos( r_x/( r_x*r_x + r_y*r_y ) )
```

It's slightly more opaque, but it's basically the dot product law:

```angle = arccos (r . v)
```

Where r and v are both unit vectors (vectors of length 1). In our case, v is the vector [1,0], and r is

```[r_x,r_y] / (r_x^2+r_y^2)
```

in order to make it a unit vector.

The x-axis is actually a line with equation

y = 0

so you could use the solution you have already.

If you need all four quadrants, Atan2 is more suitable than Atan.

```public static int GetAngleBetweenPoints(PointF pt1, PointF pt2)
{
float dx = pt2.X - pt1.X;
float dy = pt2.Y - pt1.Y;

int deg = Convert.ToInt32(Math.Atan2(dy, dx) * (180 / Math.PI));
if (deg < 0) { deg += 360; }

return deg;
}
```

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