diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index 29f11519d70d..f913013bf728 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -669,7 +669,7 @@ class Rectangle(Patch):
     """
 
     def __str__(self):
-        pars = self._x, self._y, self._width, self._height, self.angle
+        pars = self._x0, self._y0, self._width, self._height, self.angle
         fmt = "Rectangle(xy=(%g, %g), width=%g, height=%g, angle=%g)"
         return fmt % pars
 
@@ -688,10 +688,15 @@ def __init__(self, xy, width, height, angle=0.0, **kwargs):
 
         Patch.__init__(self, **kwargs)
 
-        self._x = xy[0]
-        self._y = xy[1]
+        self._x0 = xy[0]
+        self._y0 = xy[1]
+
         self._width = width
         self._height = height
+
+        self._x1 = self._x0 + self._width
+        self._y1 = self._y0 + self._height
+
         self.angle = float(angle)
         # Note: This cannot be calculated until this is added to an Axes
         self._rect_transform = transforms.IdentityTransform()
@@ -708,13 +713,13 @@ def _update_patch_transform(self):
                  maxes it very important to call the accessor method and
                  not directly access the transformation member variable.
         """
-        x = self.convert_xunits(self._x)
-        y = self.convert_yunits(self._y)
-        width = self.convert_xunits(self._width)
-        height = self.convert_yunits(self._height)
-        bbox = transforms.Bbox.from_bounds(x, y, width, height)
+        x0 = self.convert_xunits(self._x0)
+        y0 = self.convert_yunits(self._y0)
+        x1 = self.convert_xunits(self._x1)
+        y1 = self.convert_yunits(self._y1)
+        bbox = transforms.Bbox.from_extents(x0, y0, x1, y1)
         rot_trans = transforms.Affine2D()
-        rot_trans.rotate_deg_around(x, y, self.angle)
+        rot_trans.rotate_deg_around(x0, y0, self.angle)
         self._rect_transform = transforms.BboxTransformTo(bbox)
         self._rect_transform += rot_trans
 
@@ -724,15 +729,15 @@ def get_patch_transform(self):
 
     def get_x(self):
         "Return the left coord of the rectangle"
-        return self._x
+        return self._x0
 
     def get_y(self):
         "Return the bottom coord of the rectangle"
-        return self._y
+        return self._y0
 
     def get_xy(self):
         "Return the left and bottom coords of the rectangle"
-        return self._x, self._y
+        return self._x0, self._y0
 
     def get_width(self):
         "Return the width of the  rectangle"
@@ -748,7 +753,7 @@ def set_x(self, x):
 
         ACCEPTS: float
         """
-        self._x = x
+        self._x0 = x
         self.stale = True
 
     def set_y(self, y):
@@ -757,7 +762,7 @@ def set_y(self, y):
 
         ACCEPTS: float
         """
-        self._y = y
+        self._y0 = y
         self.stale = True
 
     def set_xy(self, xy):
@@ -766,7 +771,7 @@ def set_xy(self, xy):
 
         ACCEPTS: 2-item sequence
         """
-        self._x, self._y = xy
+        self._x0, self._y0 = xy
         self.stale = True
 
     def set_width(self, w):
@@ -776,6 +781,7 @@ def set_width(self, w):
         ACCEPTS: float
         """
         self._width = w
+        self._x1 = self._x0 + w
         self.stale = True
 
     def set_height(self, h):
@@ -785,6 +791,7 @@ def set_height(self, h):
         ACCEPTS: float
         """
         self._height = h
+        self._y1 = self._y0 + h
         self.stale = True
 
     def set_bounds(self, *args):
@@ -797,15 +804,17 @@ def set_bounds(self, *args):
             l, b, w, h = args[0]
         else:
             l, b, w, h = args
-        self._x = l
-        self._y = b
+        self._x0 = l
+        self._y0 = b
         self._width = w
         self._height = h
+        self._x0 = l + w
+        self._y0 = b + h
         self.stale = True
 
     def get_bbox(self):
-        return transforms.Bbox.from_bounds(self._x, self._y,
-                                           self._width, self._height)
+        return transforms.Bbox.from_extents(self._x0, self._y0,
+                                            self._x1, self._y1)
 
     xy = property(get_xy, set_xy)
 
diff --git a/lib/matplotlib/tests/test_patches.py b/lib/matplotlib/tests/test_patches.py
index 44d8b3915bcf..0dd5c3e8c282 100644
--- a/lib/matplotlib/tests/test_patches.py
+++ b/lib/matplotlib/tests/test_patches.py
@@ -364,3 +364,28 @@ def test_units_rectangle():
     ax.add_patch(p)
     ax.set_xlim([4*U.km, 7*U.km])
     ax.set_ylim([5*U.km, 9*U.km])
+
+
+def test_datetime_rectangle():
+    # Check that creating a rectangle with timedeltas doesn't fail
+    from datetime import datetime, timedelta
+
+    start = datetime(2017, 1, 1, 0, 0, 0)
+    delta = timedelta(seconds=16)
+    patch = mpatches.Rectangle((start, 0), delta, 1)
+
+    fig, ax = plt.subplots()
+    ax.add_patch(patch)
+
+
+def test_datetime_datetime_fails():
+    from datetime import datetime
+
+    start = datetime(2017, 1, 1, 0, 0, 0)
+    dt_delta = datetime(1970, 1, 5)    # Will be 5 days if units are done wrong
+
+    with pytest.raises(TypeError):
+        mpatches.Rectangle((start, 0), dt_delta, 1)
+
+    with pytest.raises(TypeError):
+        mpatches.Rectangle((0, start), 1, dt_delta)