diff --git a/django/contrib/auth/password_validation.py b/django/contrib/auth/password_validation.py
index 12cf29cb9b..4ff2c409ec 100644
--- a/django/contrib/auth/password_validation.py
+++ b/django/contrib/auth/password_validation.py
@@ -147,7 +147,7 @@ class UserAttributeSimilarityValidator(object):
                 continue
             value_parts = re.split(r'\W+', value) + [value]
             for value_part in value_parts:
-                if SequenceMatcher(a=password.lower(), b=value_part.lower()).quick_ratio() > self.max_similarity:
+                if SequenceMatcher(a=password.lower(), b=value_part.lower()).quick_ratio() >= self.max_similarity:
                     try:
                         verbose_name = force_text(user._meta.get_field(attribute_name).verbose_name)
                     except FieldDoesNotExist:
diff --git a/docs/topics/auth/passwords.txt b/docs/topics/auth/passwords.txt
index da2bc57df8..7015e65404 100644
--- a/docs/topics/auth/passwords.txt
+++ b/docs/topics/auth/passwords.txt
@@ -545,11 +545,10 @@ Django includes four validators:
     is used: ``'username', 'first_name', 'last_name', 'email'``.
     Attributes that don't exist are ignored.
 
-    The maximum similarity the password can have, before it is rejected, can
-    be set with the ``max_similarity`` parameter, on a scale of 0 to 1.
-    A setting of 0 will cause all passwords to be rejected, whereas a setting
-    of 1 will cause it to only reject passwords that are identical to an
-    attribute's value.
+    The minimum similarity of a rejected password can be set on a scale of 0 to
+    1 with the ``max_similarity`` parameter. A setting of 0 rejects all
+    passwords, whereas a setting of 1 rejects only passwords that are identical
+    to an attribute's value.
 
 .. class:: CommonPasswordValidator(password_list_path=DEFAULT_PASSWORD_LIST_PATH)
 
diff --git a/tests/auth_tests/test_validators.py b/tests/auth_tests/test_validators.py
index 97cf396b1a..e074716f46 100644
--- a/tests/auth_tests/test_validators.py
+++ b/tests/auth_tests/test_validators.py
@@ -124,7 +124,22 @@ class UserAttributeSimilarityValidatorTest(TestCase):
                 max_similarity=0.3,
             ).validate('testclient', user=user)
         self.assertEqual(cm.exception.messages, [expected_error % "first name"])
-
+        # max_similarity=1 doesn't allow passwords that are identical to the
+        # attribute's value.
+        with self.assertRaises(ValidationError) as cm:
+            UserAttributeSimilarityValidator(
+                user_attributes=['first_name'],
+                max_similarity=1,
+            ).validate(user.first_name, user=user)
+        self.assertEqual(cm.exception.messages, [expected_error % "first name"])
+        # max_similarity=0 rejects all passwords.
+        with self.assertRaises(ValidationError) as cm:
+            UserAttributeSimilarityValidator(
+                user_attributes=['first_name'],
+                max_similarity=0,
+            ).validate('XXX', user=user)
+        self.assertEqual(cm.exception.messages, [expected_error % "first name"])
+        # Passes validation.
         self.assertIsNone(
             UserAttributeSimilarityValidator(user_attributes=['first_name']).validate('testclient', user=user)
         )