diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index 78af2f98b3bf..e7ad848b3e49 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -1840,9 +1840,9 @@ def set_width(self, width):
         ----------
         width : float
         """
-        if min(self.a, self.b) <= width:
+        if width > min(self.a, self.b):
             raise ValueError(
-                'Width of annulus must be less than or equal semi-minor axis')
+                'Width of annulus must be less than or equal to semi-minor axis')
 
         self._width = width
         self._path = None