<style>
pre.ui-distance {
  position:absolute;
  bottom:10px;
  left:10px;
  padding:5px 10px;
  background:rgba(0,0,0,0.5);
  color:#fff;
  font-size:11px;
  line-height:18px;
  border-radius:3px;
  }
</style>
<div id='map'></div>
<pre id='distance' class='ui-distance'>Click to place a marker</pre>

<script>
L.mapbox.accessToken = '<your access token here>';
var map = L.mapbox.map('map', 'mapbox.streets')
    .setView([38.9, -77], 12);

// Start with a fixed marker.
var fixedMarker = L.marker(new L.LatLng(38.9131775, -77.032544), {
    icon: L.mapbox.marker.icon({
        'marker-color': 'ff8888'
    })
}).bindPopup('Mapbox DC').addTo(map);

// Store the fixedMarker coordinates in a variable.
var fc = fixedMarker.getLatLng();

// Create a featureLayer that will hold a marker and linestring.
var featureLayer = L.mapbox.featureLayer().addTo(map);

// When a user clicks on the map we want to
// create a new L.featureGroup that will contain a
// marker placed where the user selected the map and
// a linestring that draws itself between the fixedMarkers
// coordinates and the newly placed marker.
map.on('click', function(ev) {
    // ev.latlng gives us the coordinates of
    // the spot clicked on the map.
    var c = ev.latlng;

    var geojson = {
      type: 'FeatureCollection',
      features: [
        {
          "type": "Feature",
          "geometry": {
            "type": "Point",
            "coordinates": [c.lng, c.lat]
          },
          "properties": {
            "marker-color": "#ff8888"
          }
        }, {
          "type": "Feature",
          "geometry": {
            "type": "LineString",
            "coordinates": [
              [fc.lng, fc.lat],
              [c.lng, c.lat]
            ]
          },
          "properties": {
            "stroke": "#000",
            "stroke-opacity": 0.5,
            "stroke-width": 4
          }
        }
      ]
    };

    featureLayer.setGeoJSON(geojson);

    // Finally, print the distance between these two points
    // on the screen using distanceTo().
    var container = document.getElementById('distance');
    container.innerHTML = (fc.distanceTo(c)).toFixed(0) + 'm';
});
</script>