diff --git a/pydantic/fields.py b/pydantic/fields.py
index 461fe0d..e8ed386 100644
--- a/pydantic/fields.py
+++ b/pydantic/fields.py
@@ -63,6 +63,9 @@ class Field:
         if self.type_ is None:
             raise ConfigError(f'unable to infer type for attribute "{self.name}"')
 
+        if not self.required and not self.validate_always and self.default is None:
+            self.allow_none = True
+
         # typing interface is horrible, we have to do some ugly checks
         origin = getattr(self.type_, '__origin__', None)
         if origin not in (None, Union):
diff --git a/tests/test_main.py b/tests/test_main.py
index de95d28..1e1a199 100644
--- a/tests/test_main.py
+++ b/tests/test_main.py
@@ -223,3 +223,11 @@ def test_unable_to_infer():
         class InvalidDefinitionModel(BaseModel):
             x = None
     assert exc_info.value.args[0] == 'unable to infer type for attribute "x"'
+
+
+def test_not_required():
+    class Model(BaseModel):
+        a: float = None
+    assert Model(a=12.2).a == 12.2
+    assert Model().a is None
+    assert Model(a=None).a is None