diff --git a/lib/matplotlib/_afm.py b/lib/matplotlib/_afm.py
index 3d7f7a44baca..af607b0374fc 100644
--- a/lib/matplotlib/_afm.py
+++ b/lib/matplotlib/_afm.py
@@ -478,10 +478,18 @@ def get_angle(self) -> float:
         """Return the fontangle as float."""
         return self._header['ItalicAngle']
 
+    def get_ascender(self) -> float:
+        """Return the ascent as float."""
+        return self._header['Ascender']
+
     def get_capheight(self) -> float:
         """Return the cap height as float."""
         return self._header['CapHeight']
 
+    def get_descender(self) -> float:
+        """Return the descent as float."""
+        return self._header['Descender']
+
     def get_xheight(self) -> float:
         """Return the xheight as float."""
         return self._header['XHeight']
diff --git a/lib/matplotlib/backends/_backend_pdf_ps.py b/lib/matplotlib/backends/_backend_pdf_ps.py
index 83a8566517a7..a06779b8efee 100644
--- a/lib/matplotlib/backends/_backend_pdf_ps.py
+++ b/lib/matplotlib/backends/_backend_pdf_ps.py
@@ -348,6 +348,32 @@ def get_canvas_width_height(self):
         # docstring inherited
         return self.width * 72.0, self.height * 72.0
 
+    def _get_font_height_metrics(self, prop):
+        """
+        Return the ascent, descent, and line gap for font described by *prop*.
+
+        TODO: This is a temporary method until we design a proper API for the backends.
+
+        Parameters
+        ----------
+        prop : `.font_manager.FontProperties`
+            The properties describing the font to measure.
+
+        Returns
+        -------
+        ascent, descent, line_gap : float or None
+            The ascent, descent and line gap of the determined font, or None to fall
+            back to normal measurements.
+        """
+        if not mpl.rcParams[self._use_afm_rc_name]:
+            return None, None, None
+        font = self._get_font_afm(prop)
+        scale = prop.get_size_in_points() / 1000
+        a = font.get_ascender() * scale
+        d = -font.get_descender() * scale
+        g = (a + d) * 0.2  # Preserve previous line spacing of 1.2.
+        return a, d, g
+
     def get_text_width_height_descent(self, s, prop, ismath):
         # docstring inherited
         if ismath == "TeX":
diff --git a/lib/matplotlib/tests/baseline_images/test_backend_pdf/pdf_use14corefonts.pdf b/lib/matplotlib/tests/baseline_images/test_backend_pdf/pdf_use14corefonts.pdf
index 5cdc2e34e25d..b7dbb9adec70 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_backend_pdf/pdf_use14corefonts.pdf and b/lib/matplotlib/tests/baseline_images/test_backend_pdf/pdf_use14corefonts.pdf differ
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index f6ea6673ff0f..9c6478f9c7df 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -437,22 +437,29 @@ def _get_layout(self, renderer):
         dpi = self.get_figure(root=True).dpi
         # Determine full vertical extent of font, including ascenders and descenders:
         if not self.get_usetex():
-            font = get_font(fontManager._find_fonts_by_props(self._fontproperties))
-            possible_metrics = [
-                ('OS/2', 'sTypoLineGap', 'sTypoAscender', 'sTypoDescender'),
-                ('hhea', 'lineGap', 'ascent', 'descent')
-            ]
-            for table_name, linegap_key, ascent_key, descent_key in possible_metrics:
-                table = font.get_sfnt_table(table_name)
-                if table is None:
-                    continue
-                # Rescale to font size/DPI if the metrics were available.
-                fontsize = self._fontproperties.get_size_in_points()
-                units_per_em = font.get_sfnt_table('head')['unitsPerEm']
-                line_gap = table[linegap_key] / units_per_em * fontsize * dpi / 72
-                min_ascent = table[ascent_key] / units_per_em * fontsize * dpi / 72
-                min_descent = -table[descent_key] / units_per_em * fontsize * dpi / 72
-                break
+            if hasattr(renderer, '_get_font_height_metrics'):
+                # TODO: This is a temporary internal method call (for _backend_pdf_ps to
+                # support AFM files) until we design a proper API for the backends.
+                min_ascent, min_descent, line_gap = renderer._get_font_height_metrics(
+                    self._fontproperties)
+            if min_ascent is None:
+                font = get_font(fontManager._find_fonts_by_props(self._fontproperties))
+                possible = [
+                    ('OS/2', 'sTypoLineGap', 'sTypoAscender', 'sTypoDescender'),
+                    ('hhea', 'lineGap', 'ascent', 'descent')
+                ]
+                for table_name, linegap_key, ascent_key, descent_key in possible:
+                    table = font.get_sfnt_table(table_name)
+                    if table is None:
+                        continue
+                    # Rescale to font size/DPI if the metrics were available.
+                    fontsize = self._fontproperties.get_size_in_points()
+                    units_per_em = font.get_sfnt_table('head')['unitsPerEm']
+                    scale = 1 / units_per_em * fontsize * dpi / 72
+                    line_gap = table[linegap_key] * scale
+                    min_ascent = table[ascent_key] * scale
+                    min_descent = -table[descent_key] * scale
+                    break
         if None in (min_ascent, min_descent):
             # Fallback to font measurement.
             _, h, min_descent = _get_text_metrics_with_cache(