diff --git a/xarray/core/utils.py b/xarray/core/utils.py
index 5cb52cbd25c..fef3a69d8b9 100644
--- a/xarray/core/utils.py
+++ b/xarray/core/utils.py
@@ -781,8 +781,11 @@ def __iter__(self) -> Iterator[K]:
                 yield k
 
     def __len__(self) -> int:
-        num_hidden = len(self._hidden_keys & self._data.keys())
-        return len(self._data) - num_hidden
+        count = 0
+        for key in self._hidden_keys:
+            if key in self._data:
+                count += 1
+        return len(self._data) - count
 
 
 def get_temp_dimname(dims: Container[Hashable], new_dim: Hashable) -> Hashable: