title: Calculating geospatial distance with radians
body: <p>I have a method in an API that takes a lat/long coordinate and will find other coordinates within a specified distance.  That distance is in radians.  </p>
  
  <p>All the math I do these days deals with accounting or maybe x,y coordinates for laying out UI elements, so I appreciate some help validating these numbers.</p>
  
  <p>Lets ignore people in buildings (altitude) and the fact that the planet isn't perfectly spherical.  It is my understanding that the supplied method is doing the Haversine formula internally but that detail is isolated from me.</p>
  
  <p>I am looking at the <a href="http://en.wikipedia.org/wiki/Radian" rel="noreferrer">formula for radians</a>:</p>
  
  <blockquote>
    <p>θ = s /r, where θ is the subtended
    angle in radians, s is arc length, and
    r is radius</p>
  </blockquote>
  
  <p>Given the <a href="http://en.wikipedia.org/wiki/Earth_radius" rel="noreferrer">convenient mean radius of the Earth</a> of:</p>
  
  <blockquote>
    <p>6371 km
    (≈3,959 mi)</p>
  </blockquote>
  
  <p>I have seen other places saying (6378km)</p>
  
  <p>That means 1 radian on Earth is equal to 6371 km in arc length.  That would mean the radian for finding coordinates 1 meter apart would be</p>
  
  <p>( 1 / 6371 ) × 10<sup>-7</sup> <br>
  ie - 1.56961231 × 10<sup>-7</sup>.  </p>
  
  <p>Is that right?  If not where is the above incorrect?</p>