diff --git a/xarray/core/_aggregations.py b/xarray/core/_aggregations.py
index 89cec94e24f..6a111919441 100644
--- a/xarray/core/_aggregations.py
+++ b/xarray/core/_aggregations.py
@@ -1961,7 +1961,7 @@ def var(
         dim: Dims = None,
         *,
         skipna: bool | None = None,
-        ddof: int = 0,
+        ddof: int | None = None,
         keep_attrs: bool | None = None,
         **kwargs: Any,
     ) -> Self:
diff --git a/xarray/namedarray/_aggregations.py b/xarray/namedarray/_aggregations.py
index 76dfb18d068..3f8db9774d6 100644
--- a/xarray/namedarray/_aggregations.py
+++ b/xarray/namedarray/_aggregations.py
@@ -571,7 +571,7 @@ def std(
         dim: Dims = None,
         *,
         skipna: bool | None = None,
-        ddof: int = 0,
+        ddof: int | None = None,
         **kwargs: Any,
     ) -> Self:
         """