How to calculate the SVG Path for an arc (of a circle)

Question

Given a circle centered at (200,200), radius 25, how do I draw an arc from 270 degree to 135 degree and one that goes from 270 to 45 degree?

0 degree means it is right on the x-axis (the right side) (meaning it is 3 o' clock position) 270 degree means it is 12 o'clock position, and 90 means it is 6 o'clock position

More generally, what is a path for an arc for part of a circle with

x, y, r, d1, d2, direction

meaning

center (x,y), radius r, degree_start, degree_end, direction

Answer 1

Expanding on @wdebeaum's great answer, here's a method for generating an arced path:

function polarToCartesian(centerX, centerY, radius, angleInDegrees) {
  var angleInRadians = (angleInDegrees-90) * Math.PI / 180.0;

  return {
    x: centerX + (radius * Math.cos(angleInRadians)),
    y: centerY + (radius * Math.sin(angleInRadians))
  };
}

function describeArc(x, y, radius, startAngle, endAngle){

    var start = polarToCartesian(x, y, radius, endAngle);
    var end = polarToCartesian(x, y, radius, startAngle);

    var largeArcFlag = endAngle - startAngle <= 180 ? "0" : "1";

    var d = [
        "M", start.x, start.y, 
        "A", radius, radius, 0, largeArcFlag, 0, end.x, end.y
    ].join(" ");

    return d;       
}

to use

document.getElementById("arc1").setAttribute("d", describeArc(200, 400, 100, 0, 180));

and in your html

<path id="arc1" fill="none" stroke="#446688" stroke-width="20" />

Live demo