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    <p>Do you remember your trig functions? I.e. SOHCAHTOA:</p> <ul> <li><strong>SOH</strong>: Sin(θ) = Opposite over Hypotenuse</li> <li><strong>CAH</strong>: Cos(θ) = Adjacent over Hypotenuse</li> <li><strong>TOA</strong>: Tan(θ) = Opposite over Adjacent</li> </ul> <p>In pseudo-code:</p> <pre><code>function getDir(lat1, long1, lat2, long2) { margin = π/90; // 2 degree tolerance for cardinal directions o = lat1 - lat2; a = long1 - long2; angle = atan2(o,a); if (angle &gt; -margin &amp;&amp; angle &lt; margin): return "E"; elseif (angle &gt; π/2 - margin &amp;&amp; angle &lt; π/2 + margin): return "N"; elseif (angle &gt; π - margin &amp;&amp; angle &lt; -π + margin): return "W"; elseif (angle &gt; -π/2 - margin &amp;&amp; angle &lt; -π/2 + margin): return "S"; } if (angle &gt; 0 &amp;&amp; angle &lt; π/2) { return "NE"; } elseif (angle &gt; π/2 &amp;&amp; angle &lt; π) { return "NW"; } elseif (angle &gt; -π/2 &amp;&amp; angle &lt; 0) { return "SE"; } else { return "SW"; } } </code></pre> <p><strong>Edit 1:</strong> As Pete and Dean pointed out, this does not take into account the curvature of the Earth. For more accurate calculations for points away from the equator, you'll need to use <a href="http://williams.best.vwh.net/avform.htm#Crs" rel="nofollow noreferrer">spherical triangle formulas</a>, as used in Dean's answer.</p> <p><strong>Edit 2:</strong> Another correction; as Pete noted, <code>arctan()</code> does not give the correct angles, as -1/-1 and 1/1 are the same (as are -1/1 and 1/-1). <a href="http://en.wikipedia.org/wiki/Atan2" rel="nofollow noreferrer"><code>arctan2(y, x)</code></a> is a two argument variation of <code>arctan()</code> that is designed to compensate for this. <code>arctan()</code> has a range of (-π, π], positive for <code>y &gt;= 0</code> and negative for <code>y &lt; 0</code>.</p>
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    1. PODetermine compass direction from one lat/lon to the other
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    1. USLèse majesté
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    1. CO`<sup>-1</sup>`
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    2. CONote this fails the "50 miles East and one mile North is simply East and not Northeast" requirement. It also assumes you're talking about a flat plane, rather than a sphere (but that might be OK if the distances are small).
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    3. COAh, I didn't see that; will change the code.
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