# How to calculate an angle from points?

I want to get a simple solution to calculate the angle of a line (like a pointer of a clock).

I have 2 points:

``````cX, cY - the center of the line.
eX, eY - the end of the line.

The result is angle (0 <= a < 360).
``````

Which function is able to provide this value? You want the arctangent:

``````dy = ey - cy
dx = ex - cx
theta = arctan(dy/dx)
theta *= 180/pi // rads to degs
``````

Erm, note that the above is obviously not compiling Javascript code. You'll have to look through documentation for the arctangent function.

Edit: Using Math.atan2(y,x) will handle all of the special cases and extra logic for you:

``````function angle(cx, cy, ex, ey) {
var dy = ey - cy;
var dx = ex - cx;
var theta = Math.atan2(dy, dx); // range (-PI, PI]
theta *= 180 / Math.PI; // rads to degs, range (-180, 180]
//if (theta < 0) theta = 360 + theta; // range [0, 360)
return theta;
}
`````` ``````function angle(cx, cy, ex, ey) {
var dy = ey - cy;
var dx = ex - cx;
var theta = Math.atan2(dy, dx); // range (-PI, PI]
theta *= 180 / Math.PI; // rads to degs, range (-180, 180]
return theta;
}
function angle360(cx, cy, ex, ey) {
var theta = angle(cx, cy, ex, ey); // range (-180, 180]
if (theta < 0) theta = 360 + theta; // range [0, 360)
return theta;
}

show("right", 0, 0, 1, 0);
show("top right", 0, 0, 1, 1);
show("top", 0, 0, 0, 1);
show("top left", 0, 0, -1, 1);
show("left", 0, 0, -1, 0);
show("bottom left", 0, 0, -1, -1);
show("bottom", 0, 0, 0, -1);
show("bottom right", 0, 0, 1, -1);

// IGNORE BELOW HERE (all presentational stuff)``````
``````table {
border-collapse: collapse;
}
table, th, td {
border: 1px solid black;
}
tr > td:not(:first-child) {
text-align: center;
}
tfoot {
font-style: italic;
}``````
``````<table>
<tr><th>Direction*</th><th>Start</th><th>End</th><th>Angle</th><th>Angle 360</th></tr>
<tfoot>
<tr><td colspan="5">* Cartesian coordinate system<br>positive x pointing right, and positive y pointing up.</td>
</tfoot>
<tbody id="angles">
</tbody>
</table>
<script>
function show(label, cx, cy, ex, ey) {
var row = "<tr>";
row += "<td>" + label + "</td>";
row += "<td>" + [cx, cy] + "</td>";
row += "<td>" + [ex, ey] + "</td>";
row += "<td>" + angle(cx, cy, ex, ey) + "</td>";
row += "<td>" + angle360(cx, cy, ex, ey) + "</td>";
row += "</tr>";
document.getElementById("angles").innerHTML += row;
}
</script>`````` If you're using canvas, you'll notice (if you haven't already) that canvas uses clockwise rotation(MDN) and `y` axis is flipped. To get consistent results, you need to tweak your `angle` function.

From time to time, I need to write this function and each time I need to look it up, because I never get to the bottom of the calculation.

While the suggested solutions work, they don't take the canvas coordinate system into consideration. Examine the following demo:

Calculate angle from points - JSFiddle

``````function angle(originX, originY, targetX, targetY) {
var dx = originX - targetX;
var dy = originY - targetY;

// var theta = Math.atan2(dy, dx);  // [0, ?] then [-?, 0]; clockwise; 0° = west
// theta *= 180 / Math.PI;          // [0, 180] then [-180, 0]; clockwise; 0° = west
// if (theta < 0) theta += 360;     // [0, 360]; clockwise; 0° = west

// var theta = Math.atan2(-dy, dx); // [0, ?] then [-?, 0]; anticlockwise; 0° = west
// theta *= 180 / Math.PI;          // [0, 180] then [-180, 0]; anticlockwise; 0° = west
// if (theta < 0) theta += 360;     // [0, 360]; anticlockwise; 0° = west

// var theta = Math.atan2(dy, -dx); // [0, ?] then [-?, 0]; anticlockwise; 0° = east
// theta *= 180 / Math.PI;          // [0, 180] then [-180, 0]; anticlockwise; 0° = east
// if (theta < 0) theta += 360;     // [0, 360]; anticlockwise; 0° = east

var theta = Math.atan2(-dy, -dx); // [0, ?] then [-?, 0]; clockwise; 0° = east
theta *= 180 / Math.PI;           // [0, 180] then [-180, 0]; clockwise; 0° = east
if (theta < 0) theta += 360;      // [0, 360]; clockwise; 0° = east

return theta;
}
`````` One of the issue with getting the angle between two points or any angle is the reference you use.

In maths we use a trigonometric circle with the origin to the right of the circle (a point in x=radius, y=0) and count the angle counter clockwise from 0 to 2PI.

In geography the origin is the North at 0 degrees and we go clockwise from to 360 degrees.

The code below (in C#) gets the angle in radians then converts to a geographic angle:

``````    public double GetAngle()
{
var a = Math.Atan2(YEnd - YStart, XEnd - XStart);
if (a < 0) a += 2*Math.PI; //angle is now in radians

a -= (Math.PI/2); //shift by 90deg
//restore value in range 0-2pi instead of -pi/2-3pi/2
if (a < 0) a += 2*Math.PI;
if (a < 0) a += 2*Math.PI;
a = Math.Abs((Math.PI*2) - a); //invert rotation
a = a*180/Math.PI; //convert to deg

return a;
}
`````` You find here two formulas ,one from positive axis x and anticlockwise

and one from the north and clockwise.

There is x=x2-x1 and y=y2=y1 .There is E=E2-E1 and N=N2-N1.

The formulas are working for any value of x,y, E and N.

For x=y=0 or E=N=0 the result is undefined.

f(x,y)=pi()-pi()/2*(1+sign(x))*(1-sign(y^2))

``````     -pi()/4*(2+sign(x))*sign(y)

-sign(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)))
``````

f(E,N)=pi()-pi()/2*(1+sign(N))*(1-sign(E^2))

``````     -pi()/4*(2+sign(N))*sign(E)

-sign(E*N)*atan((abs(N)-abs(E))/(abs(N)+abs(E)))
``````