diff --git a/xarray/namedarray/_array_api/_utils.py b/xarray/namedarray/_array_api/_utils.py
index 777d7f84d39..49dc8a24f88 100644
--- a/xarray/namedarray/_array_api/_utils.py
+++ b/xarray/namedarray/_array_api/_utils.py
@@ -410,6 +410,8 @@ def _get_broadcasted_dims(*arrays: NamedArray[Any, Any]) -> tuple[_Dims, _Shape]
     >>> b = NamedArray(("x", "y", "z"), np.zeros((0, 3, 4)))
     >>> _get_broadcasted_dims(a, b)
     (('x', 'y', 'z'), (5, 3, 4))
+    >>> _get_broadcasted_dims(b, a)
+    (('x', 'y', 'z'), (5, 3, 4))
 
     >>> a = NamedArray(("x", "y", "z"), np.zeros((5, 3, 4)))
     >>> b = NamedArray(("x", "y", "z"), np.zeros((1, 3, 4)))
@@ -445,13 +447,17 @@ def _get_broadcasted_dims(*arrays: NamedArray[Any, Any]) -> tuple[_Dims, _Shape]
      ...
     ValueError: operands could not be broadcast together with dims = (('x', 'y', 'z'), ('x', 'y', 'z')) and shapes = ((5, 3, 4), (2, 3, 4))
     """
+    DEFAULT_SIZE = -1
+    BROADCASTABLE_SIZES = (0, 1)
+    BROADCASTABLE_SIZES_OR_DEFAULT = BROADCASTABLE_SIZES + (DEFAULT_SIZE,)
+
     arrays_dims = tuple(a.dims for a in arrays)
     arrays_shapes = tuple(a.shape for a in arrays)
 
     sizes: dict[Any, Any] = {}
     for dims, shape in zip(
         zip_longest(*map(reversed, arrays_dims), fillvalue=_default),
-        zip_longest(*map(reversed, arrays_shapes), fillvalue=-1),
+        zip_longest(*map(reversed, arrays_shapes), fillvalue=DEFAULT_SIZE),
         strict=False,
     ):
         for d, s in zip(reversed(dims), reversed(shape), strict=False):
@@ -461,8 +467,11 @@ def _get_broadcasted_dims(*arrays: NamedArray[Any, Any]) -> tuple[_Dims, _Shape]
             if s is None:
                 raise NotImplementedError("TODO: Handle None in shape, {shapes = }")
 
-            s_prev = sizes.get(d, -1)
-            if s_prev not in (-1, 0, 1, s):
+            s_prev = sizes.get(d, DEFAULT_SIZE)
+            if not (
+                s == s_prev
+                or any(v in BROADCASTABLE_SIZES_OR_DEFAULT for v in (s, s_prev))
+            ):
                 raise ValueError(
                     "operands could not be broadcast together with "
                     f"dims = {arrays_dims} and shapes = {arrays_shapes}"