BUG: pd.NA.__format__ fails with format_specs

doc/source/whatsnew/v1.1.0.rst

@@ -908,6 +908,7 @@ Missing
 - Clarified documentation on interpolate with method =akima. The ``der`` parameter must be scalar or None (:issue:`33426`)
 - :meth:`DataFrame.interpolate` uses the correct axis convention now. Previously interpolating along columns lead to interpolation along indices and vice versa. Furthermore interpolating with methods ``pad``, ``ffill``, ``bfill`` and ``backfill`` are identical to using these methods with :meth:`fillna` (:issue:`12918`, :issue:`29146`)
 - Bug in :meth:`DataFrame.interpolate` when called on a DataFrame with column names of string type was throwing a ValueError. The method is no independing of the type of column names (:issue:`33956`)
+- passing :class:`NA` will into a format string using format specs will now work. For example ``"{:.1f}".format(pd.NA)`` would previously raise a ``ValueError``, but will now return the string ``"<NA>"`` (:issue:`34740`)
 
 MultiIndex
 ^^^^^^^^^^

pandas/_libs/missing.pyx

@@ -349,6 +349,12 @@ class NAType(C_NAType):
     def __repr__(self) -> str:
         return "<NA>"
 
+    def __format__(self, format_spec) -> str:
+        try:
+            return self.__repr__().__format__(format_spec)
+        except ValueError:
+            return self.__repr__()
+
     def __bool__(self):
         raise TypeError("boolean value of NA is ambiguous")
 

pandas/tests/scalar/test_na_scalar.py

@@ -22,6 +22,17 @@ def test_repr():
     assert str(NA) == "<NA>"
 
 
+def test_format():
+    # GH-34740
+    assert format(NA) == "<NA>"
+    assert format(NA, ">10") == "      <NA>"
+    assert format(NA, "xxx") == "<NA>"  # NA is flexible, accept any format spec
+
+    assert "{}".format(NA) == "<NA>"
+    assert "{:>10}".format(NA) == "      <NA>"
+    assert "{:xxx}".format(NA) == "<NA>"
+
+
 def test_truthiness():
     msg = "boolean value of NA is ambiguous"