diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
index a52e343bb07e..a7f245d24bf4 100644
--- a/lib/matplotlib/projections/polar.py
+++ b/lib/matplotlib/projections/polar.py
@@ -399,6 +399,8 @@ def set_theta_offset(self, offset):
         """
         Set the offset for the location of 0 in radians.
         """
+        # Make sure to strip away units
+        offset = self.convert_xunits(offset)
         self._theta_offset = offset
 
     def get_theta_offset(self):
@@ -521,9 +523,17 @@ def set_thetagrids(self, angles, labels=None, frac=None, fmt=None,
         ACCEPTS: sequence of floats
         """
         # Make sure we take into account unitized data
-        angles = self.convert_yunits(angles)
-        angles = np.asarray(angles, np.float_)
-        self.set_xticks(angles * (np.pi / 180.0))
+        if isinstance( angles[0], float ):
+           # If the data is floats it is assumed to be degrees (as per the
+           # docsting for this method)
+           angles = np.asarray(angles, np.float_)
+           self.set_xticks(angles * (np.pi / 180.0))
+        else:
+           # The unit converters are defined to return radians
+           angles = self.convert_xunits(angles)
+           angles = np.asarray(angles, np.float_)
+           self.set_xticks(angles)
+
         if labels is not None:
             self.set_xticklabels(labels)
         elif fmt is not None:
@@ -560,12 +570,16 @@ def set_rgrids(self, radii, labels=None, angle=None, fmt=None,
         ACCEPTS: sequence of floats
         """
         # Make sure we take into account unitized data
-        radii = self.convert_xunits(radii)
+        radii = self.convert_yunits(radii)
         radii = np.asarray(radii)
         rmin = radii.min()
         if rmin <= 0:
             raise ValueError('radial grids must be strictly positive')
 
+        # Handle unitized data
+        if angle is not None:
+            angle = self.convert_xunits(angle)
+
         self.set_yticks(radii)
         if labels is not None:
             self.set_yticklabels(labels)
@@ -591,11 +605,21 @@ def format_coord(self, theta, r):
         Return a format string formatting the coordinate using Unicode
         characters.
         """
+        # Strip away any units
+        r = self.convert_yunits(r)
+        if not isinstance( theta, float ):
+            theta = self.convert_xunits(theta)
+            # Stripping away units makes theta be in radians.
+            # convert to degrees
+            theta = theta * (180.0 / np.pi)
+
         theta /= math.pi
         # \u03b8: lower-case theta
         # \u03c0: lower-case pi
         # \u00b0: degree symbol
-        return '\u03b8=%0.3f\u03c0 (%0.3f\u00b0), r=%0.3f' % (theta, theta * 180.0, r)
+        s = '\u03b8=%0.3f\u03c0 (%0.3f\u00b0), r=%0.3f' % (theta, theta * 180.0, r)
+        s = s.encode( 'utf-8' )
+        return s
 
     def get_data_ratio(self):
         '''
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index a2d0cad714b8..78ce2bfeceb9 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -411,6 +411,107 @@ def test_polar_units():
     assert_true(isinstance(plt.gca().get_xaxis().get_major_formatter(), units.UnitDblFormatter))
 
 
+def test_polar_format_coord():
+    import matplotlib.testing.jpl_units as units
+    units.register()
+
+    deg = units.UnitDbl(1.0, "deg")
+    km = units.UnitDbl(1.0, "km")
+
+    fig = plt.figure()
+    ax = plt.subplot(111, polar=True)
+
+    # Make sure this doesn't throw any exceptions
+    ax.format_coord( 30.0*deg, 4.0*km )
+
+
+@image_comparison(baseline_images=['polar_rgrids'])
+def test_polar_rgrids():
+    import matplotlib.testing.jpl_units as units
+    units.register()
+
+    pi = np.pi
+    deg = units.UnitDbl(1.0, "deg")
+    rad = units.UnitDbl(1.0, "rad")
+    km = units.UnitDbl(1.0, "km")
+
+    fig = plt.figure()
+
+    ax1 = plt.subplot(221, polar=True)
+    ax1.set_rgrids([45*deg, 90*deg], angle=60.0*deg)
+
+    ax2 = plt.subplot(222, polar=True)
+    ax2.set_rgrids([pi/4*rad, pi/2*rad], angle=60.0*deg)
+
+    ax3 = plt.subplot(223, polar=True)
+    ax3.set_rgrids([45*deg, 90*deg], angle=pi/3*rad)
+
+    ax4 = plt.subplot(224, polar=True)
+    ax4.set_rgrids([pi/4*rad, pi/2*rad], angle=pi/3*rad)
+
+
+@image_comparison(baseline_images=['polar_rticks'])
+def test_polar_rticks():
+    import matplotlib.testing.jpl_units as units
+    units.register()
+
+    pi = np.pi
+    deg = units.UnitDbl(1.0, "deg")
+    rad = units.UnitDbl(1.0, "rad")
+    km = units.UnitDbl(1.0, "km")
+
+    fig = plt.figure()
+
+    ax = plt.subplot(111, polar=True)
+    ax.set_rticks([1.5*km, 3.0*km, 4.5*km])
+
+    x1 = [30.0*deg, 45.0*deg, 60.0*deg, 90.0*deg]
+    y1 = [1.0*km, 2.0*km, 3.0*km, 4.0*km]
+
+    ax.plot( x1, y1 )
+
+
+@image_comparison(baseline_images=['polar_teta_offset'])
+def test_polar_theta_offset():
+    import matplotlib.testing.jpl_units as units
+    units.register()
+
+    pi = np.pi
+    deg = units.UnitDbl(1.0, "deg")
+    rad = units.UnitDbl(1.0, "rad")
+    km = units.UnitDbl(1.0, "km")
+
+    fig = plt.figure()
+
+    ax1 = plt.subplot(211, polar=True)
+    ax1.set_theta_offset(45*deg)
+
+    ax2 = plt.subplot(212, polar=True)
+    ax2.set_theta_offset(pi/4*rad)
+
+
+@image_comparison(baseline_images=['polar_tetagrids'])
+def test_polar_thetagrids():
+    import matplotlib.testing.jpl_units as units
+    units.register()
+
+    pi = np.pi
+    deg = units.UnitDbl(1.0, "deg")
+    rad = units.UnitDbl(1.0, "rad")
+    km = units.UnitDbl(1.0, "km")
+
+    fig = plt.figure()
+
+    ax1 = plt.subplot(311, polar=True)
+    ax1.set_thetagrids([90*deg, 180*deg])
+
+    ax2 = plt.subplot(312, polar=True)
+    ax2.set_thetagrids([pi/2*rad, pi*rad])
+
+    ax3 = plt.subplot(313, polar=True)
+    ax3.set_thetagrids([90.0, 180.0])
+
+
 @image_comparison(baseline_images=['polar_rmin'])
 def test_polar_rmin():
     r = np.arange(0, 3.0, 0.01)