diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 3c578d431adc..6597d70f8ac7 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -654,6 +654,7 @@ def __init__(self, axes, pickradius=15):
         # Initialize here for testing; later add API
         self._major_tick_kw = dict()
         self._minor_tick_kw = dict()
+        self._tick_space = None
 
         self.cla()
         self._set_scale('linear')
@@ -785,6 +786,7 @@ def set_tick_params(self, which='major', reset=False, **kw):
                 for tick in self.minorTicks:
                     tick._apply_params(**self._minor_tick_kw)
         self.stale = True
+        self._tick_space = None
 
     @staticmethod
     def _translate_tick_kw(kw, to_init_kw=True):
@@ -1665,6 +1667,13 @@ def axis_date(self, tz=None):
             tz = pytz.timezone(tz)
         self.update_units(datetime.datetime(2009, 1, 1, 0, 0, 0, 0, tz))
 
+    def get_tick_space(self):
+        """
+        Return the estimated number of ticks that can fit on the axis.
+        """
+        # Must be overridden in the subclass
+        raise NotImplementedError()
+
 
 class XAxis(Axis):
     __name__ = 'xaxis'
@@ -1988,6 +1997,18 @@ def set_default_intervals(self):
                 self.axes.viewLim.intervalx = xmin, xmax
         self.stale = True
 
+    def get_tick_space(self):
+        if self._tick_space is None:
+            ends = self.axes.transAxes.transform([[0, 0], [1, 0]])
+            length = ((ends[1][0] - ends[0][0]) / self.axes.figure.dpi) * 72.0
+            tick = self._get_tick(True)
+            # There is a heuristic here that the aspect ratio of tick text
+            # is no more than 3:1
+            size = tick.label1.get_size() * 3
+            size *= np.cos(np.deg2rad(tick.label1.get_rotation()))
+            self._tick_space = np.floor(length / size)
+        return self._tick_space
+
 
 class YAxis(Axis):
     __name__ = 'yaxis'
@@ -2318,3 +2339,14 @@ def set_default_intervals(self):
             if not viewMutated:
                 self.axes.viewLim.intervaly = ymin, ymax
         self.stale = True
+
+    def get_tick_space(self):
+        if self._tick_space is None:
+            ends = self.axes.transAxes.transform([[0, 0], [0, 1]])
+            length = ((ends[1][1] - ends[0][1]) / self.axes.figure.dpi) * 72.0
+            tick = self._get_tick(True)
+            # Having a spacing of at least 2 just looks good.
+            size = tick.label1.get_size() * 2.0
+            size *= np.cos(np.deg2rad(tick.label1.get_rotation()))
+            self._tick_space = np.floor(length / size)
+        return self._tick_space
diff --git a/lib/matplotlib/tests/baseline_images/test_artist/default_edges.png b/lib/matplotlib/tests/baseline_images/test_artist/default_edges.png
index 074f1bf404d9..612eb3dd3c48 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_artist/default_edges.png and b/lib/matplotlib/tests/baseline_images/test_artist/default_edges.png differ
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/auto_numticks.png b/lib/matplotlib/tests/baseline_images/test_axes/auto_numticks.png
new file mode 100644
index 000000000000..91d220768457
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_axes/auto_numticks.png differ
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 3a1a25053da5..b91c6553c348 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -4191,6 +4191,12 @@ def test_axes_margins():
     assert ax.get_ybound() == (-0.5, 9.5)
 
 
+@image_comparison(baseline_images=["auto_numticks"], style='default',
+                  extensions=['png'])
+def test_auto_numticks():
+    fig, axes = plt.subplots(4, 4)
+
+
 if __name__ == '__main__':
     import nose
     import sys
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index b487671fb5e9..2c7ce1f62b1b 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -202,6 +202,10 @@ def get_data_interval(self):
     def set_data_interval(self, vmin, vmax):
         self.dataLim.intervalx = vmin, vmax
 
+    def get_tick_space(self):
+        # Just use the long-standing default of nbins==9
+        return 9
+
 
 class TickHelper(object):
     axis = None
@@ -1349,7 +1353,9 @@ def __init__(self, *args, **kwargs):
         Keyword args:
 
         *nbins*
-            Maximum number of intervals; one less than max number of ticks.
+            Maximum number of intervals; one less than max number of
+            ticks.  If the string `'auto'`, the number of bins will be
+            automatically determined based on the length of the axis.
 
         *steps*
             Sequence of nice numbers starting with 1 and ending with 10;
@@ -1387,7 +1393,9 @@ def __init__(self, *args, **kwargs):
     def set_params(self, **kwargs):
         """Set parameters within this locator."""
         if 'nbins' in kwargs:
-            self._nbins = int(kwargs['nbins'])
+            self._nbins = kwargs['nbins']
+            if self._nbins != 'auto':
+                self._nbins = int(self._nbins)
         if 'trim' in kwargs:
             self._trim = kwargs['trim']
         if 'integer' in kwargs:
@@ -1416,6 +1424,8 @@ def set_params(self, **kwargs):
 
     def bin_boundaries(self, vmin, vmax):
         nbins = self._nbins
+        if nbins == 'auto':
+            nbins = self.axis.get_tick_space()
         scale, offset = scale_range(vmin, vmax, nbins)
         if self._integer:
             scale = max(1, scale)
@@ -1901,7 +1911,11 @@ def tick_values(self, vmin, vmax):
 
 class AutoLocator(MaxNLocator):
     def __init__(self):
-        MaxNLocator.__init__(self, nbins=9, steps=[1, 2, 5, 10])
+        if rcParams['_internal.classic_mode']:
+            nbins = 9
+        else:
+            nbins = 'auto'
+        MaxNLocator.__init__(self, nbins=nbins, steps=[1, 2, 5, 10])
 
 
 class AutoMinorLocator(Locator):