diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index a8c81b05df73..bc5257bab60e 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -2157,7 +2157,7 @@ def print_figure(self, filename, dpi=None, facecolor=None, edgecolor=None,
             dpi = rcParams['savefig.dpi']
 
         if dpi == 'figure':
-            dpi = self.figure.dpi
+            dpi = getattr(self.figure, '_original_dpi', self.figure.dpi)
 
         if facecolor is None:
             facecolor = rcParams['savefig.facecolor']
diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 0c71385eb338..4041991bd757 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -149,7 +149,11 @@ def _create_qApp():
             qApp = app
 
     if is_pyqt5():
-        qApp.setAttribute(QtCore.Qt.AA_UseHighDpiPixmaps)
+        try:
+            qApp.setAttribute(QtCore.Qt.AA_UseHighDpiPixmaps)
+            qApp.setAttribute(QtCore.Qt.AA_EnableHighDpiScaling)
+        except AttributeError:
+            pass
 
 
 class Show(ShowBase):
@@ -159,6 +163,7 @@ def mainloop(self):
         global qApp
         qApp.exec_()
 
+
 show = Show()
 
 
@@ -261,17 +266,20 @@ def leaveEvent(self, event):
         FigureCanvasBase.leave_notify_event(self, guiEvent=event)
 
     def mouseEventCoords(self, pos):
-        """
-        Calculate mouse coordinates in logical pixels.
+        """Calculate mouse coordinates in physical pixels
+
+        Qt5 use logical pixels, but the figure is scaled to physical
+        pixels for rendering.   Transform to physical pixels so that
+        all of the down-stream transforms work as expected.
+
+        Also, the origin is different and needs to be corrected.
 
-        Qt5 and Matplotlib use logical pixels, but the figure is scaled to
-        physical pixels for rendering. Also, the origin is different and needs
-        to be corrected.
         """
+        dpi_ratio = self._dpi_ratio
         x = pos.x()
         # flip y so y=0 is bottom of canvas
-        y = self.figure.bbox.height / self._dpi_ratio - pos.y()
-        return x, y
+        y = self.figure.bbox.height / dpi_ratio - pos.y()
+        return x * dpi_ratio, y * dpi_ratio
 
     def mousePressEvent(self, event):
         x, y = self.mouseEventCoords(event.pos())
@@ -579,7 +587,9 @@ def __init__(self, canvas, parent, coordinates=True):
     def _icon(self, name):
         if is_pyqt5():
             name = name.replace('.png', '_large.png')
-        return QtGui.QIcon(os.path.join(self.basedir, name))
+        pm = QtGui.QPixmap(os.path.join(self.basedir, name))
+        pm.setDevicePixelRatio(self.canvas._dpi_ratio)
+        return QtGui.QIcon(pm)
 
     def _init_toolbar(self):
         self.basedir = os.path.join(matplotlib.rcParams['datapath'], 'images')
@@ -589,7 +599,7 @@ def _init_toolbar(self):
                 self.addSeparator()
             else:
                 a = self.addAction(self._icon(image_file + '.png'),
-                                         text, getattr(self, callback))
+                                   text, getattr(self, callback))
                 self._actions[callback] = a
                 if callback in ['zoom', 'pan']:
                     a.setCheckable(True)
@@ -611,7 +621,7 @@ def _init_toolbar(self):
                     QtCore.Qt.AlignRight | QtCore.Qt.AlignTop)
             self.locLabel.setSizePolicy(
                 QtWidgets.QSizePolicy(QtWidgets.QSizePolicy.Expanding,
-                                  QtWidgets.QSizePolicy.Ignored))
+                                      QtWidgets.QSizePolicy.Ignored))
             labelAction = self.addWidget(self.locLabel)
             labelAction.setVisible(True)
 
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index 8f3b3afe7c03..288ff450a25e 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -323,9 +323,10 @@ def __init__(self,
         if frameon is None:
             frameon = rcParams['figure.frameon']
 
-        self.dpi_scale_trans = Affine2D()
-        self.dpi = dpi
         self.bbox_inches = Bbox.from_bounds(0, 0, *figsize)
+        self.dpi_scale_trans = Affine2D().scale(dpi, dpi)
+        # do not use property as it will trigger
+        self._dpi = dpi
         self.bbox = TransformedBbox(self.bbox_inches, self.dpi_scale_trans)
 
         self.frameon = frameon
@@ -413,6 +414,7 @@ def _get_dpi(self):
     def _set_dpi(self, dpi):
         self._dpi = dpi
         self.dpi_scale_trans.clear().scale(dpi, dpi)
+        self.set_size_inches(*self.get_size_inches())
         self.callbacks.process('dpi_changed', self)
     dpi = property(_get_dpi, _set_dpi)
 
@@ -710,13 +712,15 @@ def set_size_inches(self, w, h=None, forward=True):
         self.bbox_inches.p1 = w, h
 
         if forward:
-            ratio = getattr(self.canvas, '_dpi_ratio', 1)
-            dpival = self.dpi / ratio
-            canvasw = w * dpival
-            canvash = h * dpival
-            manager = getattr(self.canvas, 'manager', None)
-            if manager is not None:
-                manager.resize(int(canvasw), int(canvash))
+            canvas = getattr(self, 'canvas')
+            if canvas is not None:
+                ratio = getattr(self.canvas, '_dpi_ratio', 1)
+                dpival = self.dpi / ratio
+                canvasw = w * dpival
+                canvash = h * dpival
+                manager = getattr(self.canvas, 'manager', None)
+                if manager is not None:
+                    manager.resize(int(canvasw), int(canvash))
         self.stale = True
 
     def get_size_inches(self):
diff --git a/lib/matplotlib/tests/test_figure.py b/lib/matplotlib/tests/test_figure.py
index 677bf50da23e..f5ce06b0d942 100644
--- a/lib/matplotlib/tests/test_figure.py
+++ b/lib/matplotlib/tests/test_figure.py
@@ -214,6 +214,18 @@ def test_figaspect():
     assert h / w == 1
 
 
+@cleanup(style='default')
+def test_change_dpi():
+    fig = plt.figure(figsize=(4, 4))
+    fig.canvas.draw()
+    assert fig.canvas.renderer.height == 400
+    assert fig.canvas.renderer.width == 400
+    fig.dpi = 50
+    fig.canvas.draw()
+    assert fig.canvas.renderer.height == 200
+    assert fig.canvas.renderer.width == 200
+
+
 if __name__ == "__main__":
     import nose
     nose.runmodule(argv=['-s', '--with-doctest'], exit=False)