diff --git a/lib/cartopy/crs.py b/lib/cartopy/crs.py
index aadc6cd9f..f193cbda2 100644
--- a/lib/cartopy/crs.py
+++ b/lib/cartopy/crs.py
@@ -2329,7 +2329,7 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
         maxs = np.max(coords, axis=1)
         self._x_limits = mins[0], maxs[0]
         self._y_limits = mins[1], maxs[1]
-        self._threshold = min(a, b) / 63.78137  # About 1e5 for defaults.
+        self._threshold = min(a, b) * 1.5e-3  # Approximately 1e4 for defaults.
 
     @property
     def boundary(self):