diff --git a/dm_control/utils/inverse_kinematics.py b/dm_control/utils/inverse_kinematics.py
index 623d2ea9..7cb3073d 100644
--- a/dm_control/utils/inverse_kinematics.py
+++ b/dm_control/utils/inverse_kinematics.py
@@ -213,6 +213,20 @@ def qpos_from_site_pose(physics,
       logging.debug('Step %2i: err_norm=%-10.3g update_norm=%-10.3g',
                     steps, err_norm, update_norm)
 
+  # The final permitted update may reach the target. Report the residual
+  # of the returned configuration rather than the preceding configuration.
+  err_norm = 0.0
+  if target_pos is not None:
+    err_pos[:] = target_pos - site_xpos
+    err_norm += np.linalg.norm(err_pos)
+  if target_quat is not None:
+    mjlib.mju_mat2Quat(site_xquat, site_xmat)
+    mjlib.mju_negQuat(neg_site_xquat, site_xquat)
+    mjlib.mju_mulQuat(err_rot_quat, target_quat, neg_site_xquat)
+    mjlib.mju_quat2Vel(err_rot, err_rot_quat, 1)
+    err_norm += np.linalg.norm(err_rot) * rot_weight
+  success = err_norm < tol
+
   if not success and steps == max_steps - 1:
     logging.warning('Failed to converge after %i steps: err_norm=%3g',
                     steps, err_norm)
diff --git a/dm_control/utils/inverse_kinematics_final_residual_test.py b/dm_control/utils/inverse_kinematics_final_residual_test.py
new file mode 100644
index 00000000..9a7d24ec
--- /dev/null
+++ b/dm_control/utils/inverse_kinematics_final_residual_test.py
@@ -0,0 +1,99 @@
+"""IK result residuals and convergence describe the returned physical pose."""
+import math
+
+from absl.testing import absltest
+from dm_control import mujoco
+from dm_control.utils import inverse_kinematics as ik
+import numpy as np
+
+
+_XML = """
+<mujoco>
+  <worldbody>
+    <body>
+      <joint name="x" type="slide" axis="1 0 0"/>
+      <joint name="y" type="slide" axis="0 1 0"/>
+      <joint name="z" type="slide" axis="0 0 1"/>
+      <joint name="yaw" type="hinge" axis="0 0 1"/>
+      <geom type="sphere" size="0.01" mass="1"/>
+      <site name="tip" size="0.005"/>
+    </body>
+  </worldbody>
+</mujoco>
+"""
+
+
+class FinalResidualTest(absltest.TestCase):
+
+  def _result(self, target_pos=None, angle=None, inplace=False, **kwargs):
+    physics = mujoco.Physics.from_xml_string(_XML)
+    target_quat = None if angle is None else np.array([
+        math.cos(angle / 2), 0., 0., math.sin(angle / 2)])
+    result = ik.qpos_from_site_pose(
+        physics, 'tip', target_pos=target_pos, target_quat=target_quat,
+        max_steps=1, tol=1e-10, inplace=inplace, **kwargs)
+    if not inplace:
+      np.testing.assert_array_equal(physics.data.qpos, np.zeros(4))
+    physics.data.qpos[:] = result.qpos
+    physics.forward()
+    # Independent geometry: translation distance and signed planar angle.
+    # Do not reuse the solver's quaternion residual implementation.
+    actual_error = 0.
+    if target_pos is not None:
+      actual_error += np.linalg.norm(
+          np.asarray(target_pos) - physics.named.data.site_xpos['tip'])
+    if angle is not None:
+      matrix = physics.named.data.site_xmat['tip'].reshape(3, 3)
+      actual_angle = math.atan2(matrix[1, 0], matrix[0, 0])
+      difference = math.atan2(math.sin(angle - actual_angle),
+                              math.cos(angle - actual_angle))
+      actual_error += abs(difference) * kwargs.get('rot_weight', 1.)
+    self.assertAlmostEqual(float(result.err_norm), actual_error, places=12)
+    self.assertEqual(bool(result.success), actual_error < 1e-10)
+    return result, physics
+
+  def test_last_permitted_translation_update_can_converge(self):
+    for inplace in (False, True):
+      with self.subTest(inplace=inplace):
+        result, _ = self._result(target_pos=[.01, -.02, .03], inplace=inplace)
+        np.testing.assert_allclose(result.qpos[:3], [.01, -.02, .03], atol=1e-12)
+        self.assertTrue(result.success)
+
+  def test_last_permitted_rotation_update_can_converge(self):
+    for inplace in (False, True):
+      with self.subTest(inplace=inplace):
+        result, _ = self._result(angle=.04, inplace=inplace)
+        self.assertAlmostEqual(result.qpos[3], .04, places=12)
+        self.assertTrue(result.success)
+
+  def test_combined_pose_uses_final_weighted_error(self):
+    result, _ = self._result(target_pos=[.01, -.02, .03], angle=.04,
+                             rot_weight=.7)
+    self.assertTrue(result.success)
+
+  def test_clipped_update_reports_remaining_error_without_success(self):
+    result, _ = self._result(target_pos=[.02, 0., 0.], max_update_norm=.005)
+    self.assertAlmostEqual(result.err_norm, .015, places=12)
+    self.assertFalse(result.success)
+
+  def test_regularized_update_reports_remaining_error_without_success(self):
+    result, _ = self._result(target_pos=[.4, 0., 0.])
+    self.assertAlmostEqual(result.qpos[0], .4 / 1.03, places=12)
+    self.assertAlmostEqual(result.err_norm, .4 - .4 / 1.03, places=12)
+    self.assertFalse(result.success)
+
+  def test_already_converged_configuration_is_unchanged(self):
+    result, _ = self._result(target_pos=[0., 0., 0.], angle=0.)
+    np.testing.assert_array_equal(result.qpos, np.zeros(4))
+    self.assertEqual(result.err_norm, 0.)
+    self.assertTrue(result.success)
+
+  def test_progress_termination_reports_unmodified_configuration(self):
+    result, _ = self._result(target_pos=[.02, 0., 0.], progress_thresh=.5)
+    np.testing.assert_array_equal(result.qpos, np.zeros(4))
+    self.assertAlmostEqual(result.err_norm, .02, places=12)
+    self.assertFalse(result.success)
+
+
+if __name__ == '__main__':
+  absltest.main()