diff --git a/lib/matplotlib/tests/test_text.py b/lib/matplotlib/tests/test_text.py
index 83b65be400db..d2a7865df8ff 100644
--- a/lib/matplotlib/tests/test_text.py
+++ b/lib/matplotlib/tests/test_text.py
@@ -753,6 +753,49 @@ def test_wrap_no_wrap():
     assert text._get_wrapped_text() == 'non wrapped text'
 
 
+@pytest.mark.parametrize(
+    "x, y, rotation",
+    [(0.0, 1.0, 0),
+     (1.0, 0.5, 90),
+     (0.5, 1.0, 180),
+     (0.0, 0.5, 270)])
+def test_wrap_on_figure_edge(x, y, rotation):
+    # Regression test for #31537 - wrap collapsed to zero on figure edges.
+    s = 'This is a very long text that should be wrapped multiple times.'
+    fig = plt.figure(figsize=(6, 4))
+    t = fig.text(x, y, s, wrap=True, rotation=rotation)
+    fig.canvas.draw()
+
+    # Compare to a nudged-off-the-edge reference that should wrap the same.
+    nudge = 1e-4
+    x_ref = x - nudge if x == 1.0 else x + nudge if x == 0.0 else x
+    y_ref = y - nudge if y == 1.0 else y + nudge if y == 0.0 else y
+    fig_ref = plt.figure(figsize=(6, 4))
+    t_ref = fig_ref.text(x_ref, y_ref, s, wrap=True, rotation=rotation)
+    fig_ref.canvas.draw()
+
+    assert t._get_wrapped_text() == t_ref._get_wrapped_text()
+
+
+def test_wrap_on_figure_edge_transform_rotates_text():
+    # Regression test for #31537 - transform_rotates_text with an axis-aligned
+    # transform can make get_rotation() float-round to 360.0.
+    s = 'This is a very long text that should be wrapped multiple times.'
+
+    fig = plt.figure(figsize=(6, 4))
+    transform = mtransforms.Affine2D().rotate_deg(270) + fig.transFigure
+    t = fig.text(0.0, 0.0, s, transform=transform, wrap=True,
+                 rotation=90, transform_rotates_text=True)
+    fig.canvas.draw()
+
+    fig_ref = plt.figure(figsize=(6, 4))
+    t_ref = fig_ref.text(0.0, 0.0, s, wrap=True, rotation=0)
+    fig_ref.canvas.draw()
+
+    assert 0 <= t.get_rotation() < 360
+    assert t._get_wrapped_text() == t_ref._get_wrapped_text()
+
+
 @check_figures_equal()
 def test_buffer_size(fig_test, fig_ref):
     # On old versions of the Agg renderer, large non-ascii single-character
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index 9c6478f9c7df..a17a01d195d6 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -339,8 +339,10 @@ def _char_index_at(self, x):
     def get_rotation(self):
         """Return the text angle in degrees in the range [0, 360)."""
         if self.get_transform_rotates_text():
-            return self.get_transform().transform_angles(
+            angle = self.get_transform().transform_angles(
                 [self._rotation], [self.get_unitless_position()]).item(0) % 360
+            # `(tiny_negative) % 360` can float-round to exactly 360.0.
+            return 0.0 if angle == 360 else angle
         else:
             return self._rotation
 
@@ -757,6 +759,17 @@ def _get_dist_to_box(self, rotation, x0, y0, figure_box):
         Return the distance from the given points to the boundaries of a
         rotated box, in pixels.
         """
+        # Short-circuit cardinals; otherwise cos(radians(90)) makes the trig
+        # formula below blow up when the text is on the matching edge.
+        if rotation == 0:
+            return figure_box.x1 - x0
+        if rotation == 90:
+            return figure_box.y1 - y0
+        if rotation == 180:
+            return x0 - figure_box.x0
+        if rotation == 270:
+            return y0 - figure_box.y0
+
         if rotation > 270:
             quad = rotation - 270
             h1 = (y0 - figure_box.y0) / math.cos(math.radians(quad))