diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 5d522cd0988a..10f693ace0cf 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -1568,10 +1568,11 @@ def _on_move(self, event):
             q = _Quaternion.from_cardan_angles(elev, azim, roll)
 
             # Update quaternion - a variation on Ken Shoemake's ARCBALL
-            current_vec = self._arcball(self._sx/w, self._sy/h)
-            new_vec = self._arcball(x/w, y/h)
+            scale = np.sqrt(2)/2  # slow down the rate of rotation
+            current_vec = self._arcball(self._sx*scale/w, self._sy*scale/h)
+            new_vec = self._arcball(x*scale/w, y*scale/h)
             dq = _Quaternion.rotate_from_to(current_vec, new_vec)
-            q = dq * q
+            q = dq * dq * q
 
             # Convert to elev, azim, roll
             elev, azim, roll = q.as_cardan_angles()
@@ -4020,11 +4021,14 @@ def from_cardan_angles(cls, elev, azim, roll):
     def as_cardan_angles(self):
         """
         The inverse of `from_cardan_angles()`.
+        This function acts on the quaternion as if it were unit normed.
         Note that the angles returned are in radians, not degrees.
         """
         qw = self.scalar
         qx, qy, qz = self.vector[..., :]
         azim = np.arctan2(2*(-qw*qz+qx*qy), qw*qw+qx*qx-qy*qy-qz*qz)
-        elev = np.arcsin( 2*( qw*qy+qz*qx)/(qw*qw+qx*qx+qy*qy+qz*qz))  # noqa E201
+        # Clip below is to avoid floating point round-off errors
+        elev = np.arcsin(np.clip(2*(qw*qy+qz*qx)
+                                  / (qw*qw+qx*qx+qy*qy+qz*qz), -1, 1))
         roll = np.arctan2(2*( qw*qx-qy*qz), qw*qw-qx*qx-qy*qy+qz*qz)   # noqa E201
         return elev, azim, roll
diff --git a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
index 0afcae99c980..07ecb0086030 100644
--- a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
@@ -1950,10 +1950,10 @@ def test_rotate():
     for roll, dx, dy, new_elev, new_azim, new_roll in [
             [0, 0.5, 0, 0, -90, 0],
             [30, 0.5, 0, 30, -90, 0],
-            [0, 0, 0.5, -90, 0, 0],
+            [0, 0, 0.5, -90, -180, 180],
             [30, 0, 0.5, -60, -90, 90],
-            [0, 0.5, 0.5, -45, -90, 45],
-            [30, 0.5, 0.5, -15, -90, 45]]:
+            [0, np.sqrt(2)/4, np.sqrt(2)/4, -45, -90, 45],
+            [30, np.sqrt(2)/4, np.sqrt(2)/4, -15, -90, 45]]:
         fig = plt.figure()
         ax = fig.add_subplot(1, 1, 1, projection='3d')
         ax.view_init(0, 0, roll)
@@ -1967,9 +1967,8 @@ def test_rotate():
                            xdata=dx*ax._pseudo_w, ydata=dy*ax._pseudo_h))
         fig.canvas.draw()
 
-        assert np.isclose(ax.elev, new_elev)
-        assert np.isclose(ax.azim, new_azim)
-        assert np.isclose(ax.roll, new_roll)
+        np.testing.assert_allclose((ax.elev, ax.azim, ax.roll),
+                                   (new_elev, new_azim, new_roll), atol=1e-6)
 
 
 def test_pan():