diff --git a/doc/users/next_whats_new/2020-03-24-svg-hatch-alpha.rst b/doc/users/next_whats_new/2020-03-24-svg-hatch-alpha.rst
diff --git a/doc/users/next_whats_new/hatch-alpha.rst b/doc/users/next_whats_new/hatch-alpha.rst
@@ -0,0 +1,6 @@
+The SVG and PDF backends can now render hatches with transparency
+-----------------------------------------------------------------
+
+The SVG and PDF backends now respect the hatch stroke alpha. Useful applications
+are, among others, semi-transparent hatches as a subtle way to differentiate
+columns in bar plots.
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
@@ -1288,14 +1288,18 @@ def _write_soft_mask_groups(self):
             self.output(*content)
             self.endStream()
 
-    def hatchPattern(self, hatch_style):
+    def hatchPattern(self, hatch_style, forced_alpha):
         # The colors may come in as numpy arrays, which aren't hashable
         if hatch_style is not None:
             edge, face, hatch = hatch_style
             if edge is not None:
                 edge = tuple(edge)
+                if forced_alpha:  # reset alpha if forced
+                    edge = edge[:3] + (1.0,)
             if face is not None:
                 face = tuple(face)
+                if forced_alpha:  # reset alpha if forced
+                    face = face[:3] + (1.0,)
             hatch_style = (edge, face, hatch)
 
         pattern = self.hatchPatterns.get(hatch_style, None)
@@ -1310,10 +1314,14 @@ def writeHatches(self):
         hatchDict = dict()
         sidelen = 72.0
         for hatch_style, name in self.hatchPatterns.items():
+            stroke_rgb, fill_rgb, path = hatch_style
             ob = self.reserveObject('hatch pattern')
             hatchDict[name] = ob
             res = {'Procsets':
                    [Name(x) for x in "PDF Text ImageB ImageC ImageI".split()]}
+            if stroke_rgb[3] != 1.0:
+                res['ExtGState'] = self._extGStateObject
+
             self.beginStream(
                 ob.id, None,
                 {'Type': Name('Pattern'),
@@ -1324,7 +1332,9 @@ def writeHatches(self):
                  # Change origin to match Agg at top-left.
                  'Matrix': [1, 0, 0, 1, 0, self.height * 72]})
 
-            stroke_rgb, fill_rgb, path = hatch_style
+            if stroke_rgb[3] != 1.0:
+                gstate = self.alphaState((stroke_rgb[3], fill_rgb[3]))
+                self.output(gstate, Op.setgstate)
             self.output(stroke_rgb[0], stroke_rgb[1], stroke_rgb[2],
                         Op.setrgb_stroke)
             if fill_rgb is not None:
@@ -2245,15 +2255,15 @@ def alpha_cmd(self, alpha, forced, effective_alphas):
         name = self.file.alphaState(effective_alphas)
         return [name, Op.setgstate]
 
-    def hatch_cmd(self, hatch, hatch_color):
+    def hatch_cmd(self, hatch, hatch_color, forced_alpha):
         if not hatch:
             if self._fillcolor is not None:
                 return self.fillcolor_cmd(self._fillcolor)
             else:
                 return [Name('DeviceRGB'), Op.setcolorspace_nonstroke]
         else:
             hatch_style = (hatch_color, self._fillcolor, hatch)
-            name = self.file.hatchPattern(hatch_style)
+            name = self.file.hatchPattern(hatch_style, forced_alpha)
             return [Name('Pattern'), Op.setcolorspace_nonstroke,
                     name, Op.setcolor_nonstroke]
 
@@ -2311,13 +2321,15 @@ def clip_cmd(self, cliprect, clippath):
         (('_cliprect', '_clippath'), clip_cmd),
         (('_alpha', '_forced_alpha', '_effective_alphas'), alpha_cmd),
         (('_capstyle',), capstyle_cmd),
+        # If you change the next line also fix the check in delta
         (('_fillcolor',), fillcolor_cmd),
         (('_joinstyle',), joinstyle_cmd),
         (('_linewidth',), linewidth_cmd),
         (('_dashes',), dash_cmd),
         (('_rgb',), rgb_cmd),
         # must come after fillcolor and rgb
-        (('_hatch', '_hatch_color'), hatch_cmd),
+        # If you change the next line also fix the check in delta
+        (('_hatch', '_hatch_color', '_forced_alpha'), hatch_cmd),
         )
 
     def delta(self, other):
@@ -2346,7 +2358,8 @@ def delta(self, other):
                     break
 
             # Need to update hatching if we also updated fillcolor
-            if params == ('_hatch', '_hatch_color') and fill_performed:
+            if (params == ('_hatch', '_hatch_color', '_forced_alpha')
+                    and fill_performed):
                 different = True
 
             if different:

diff --git a/lib/matplotlib/backends/backend_svg.py b/lib/matplotlib/backends/backend_svg.py
@@ -350,12 +350,17 @@ def _get_hatch(self, gc, rgbFace):
         """
         Create a new hatch pattern
         """
+        forced_alpha = gc.get_forced_alpha()
         if rgbFace is not None:
             rgbFace = tuple(rgbFace)
+            if forced_alpha:  # reset alpha if forced
+                rgbFace = rgbFace[:3] + (1.0,)
         edge = gc.get_hatch_color()
         if edge is not None:
             edge = tuple(edge)
-        dictkey = (gc.get_hatch(), rgbFace, edge)
+            if forced_alpha:  # reset alpha if forced
+                edge = edge[:3] + (1.0,)
+        dictkey = (gc.get_hatch(), rgbFace, edge, gc.get_forced_alpha())
         oid = self._hatchd.get(dictkey)
         if oid is None:
             oid = self._make_id('h', dictkey)
@@ -398,8 +403,8 @@ def _write_hatches(self):
                     'stroke-linecap': 'butt',
                     'stroke-linejoin': 'miter'
                     }
-            if stroke[3] < 1:
-                hatch_style['stroke-opacity'] = str(stroke[3])
+            if stroke[3] != 1.0:
+                hatch_style['stroke-opacity'] = short_float_fmt(stroke[3])
             writer.element(
                 'path',
                 d=path_data,

diff --git a/lib/matplotlib/collections.py b/lib/matplotlib/collections.py
@@ -299,6 +299,7 @@ def draw(self, renderer):
         gc = renderer.new_gc()
         self._set_gc_clip(gc)
         gc.set_snap(self.get_snap())
+        gc.set_alpha(self._alpha)
 
         if self._hatch:
             gc.set_hatch(self._hatch)

diff --git a/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.pdf b/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.pdf
diff --git a/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.png b/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.png
diff --git a/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.svg b/lib/matplotlib/tests/baseline_images/test_artist/clip_path_clipping.svg
diff --git a/lib/matplotlib/tests/baseline_images/test_artist/hatching.pdf b/lib/matplotlib/tests/baseline_images/test_artist/hatching.pdf
diff --git a/lib/matplotlib/tests/baseline_images/test_artist/hatching.png b/lib/matplotlib/tests/baseline_images/test_artist/hatching.png