diff --git a/crates/polars-core/src/frame/mod.rs b/crates/polars-core/src/frame/mod.rs
index a72da39d915d..dae71dd44ff0 100644
--- a/crates/polars-core/src/frame/mod.rs
+++ b/crates/polars-core/src/frame/mod.rs
@@ -813,6 +813,12 @@ impl DataFrame {
         self.shape().0
     }
 
+    /// Returns the size as number of rows * number of columns
+    pub fn size(&self) -> usize {
+        let s = self.shape();
+        s.0 * s.1
+    }
+
     /// Returns `true` if the [`DataFrame`] contains no rows.
     ///
     /// # Example
diff --git a/crates/polars-mem-engine/src/executors/stack.rs b/crates/polars-mem-engine/src/executors/stack.rs
index 43c884b1f563..074bcbaf9e79 100644
--- a/crates/polars-mem-engine/src/executors/stack.rs
+++ b/crates/polars-mem-engine/src/executors/stack.rs
@@ -66,7 +66,7 @@ impl StackExec {
                 // possibly mismatching column lengths.
                 unsafe { df.get_columns_mut() }.extend(res.into_iter().map(Column::from));
             } else {
-                let height = df.height();
+                let (df_height, df_width) = df.shape();
 
                 // When we have CSE we cannot verify scalars yet.
                 let verify_scalar = if !df.get_columns().is_empty() {
@@ -78,11 +78,11 @@ impl StackExec {
                 };
                 for (i, c) in res.iter().enumerate() {
                     let len = c.len();
-                    if verify_scalar && len != height && len == 1 {
+                    if verify_scalar && len != df_height && len == 1 && df_width > 0 {
                         polars_ensure!(self.exprs[i].is_scalar(),
                             InvalidOperation: "Series {}, length {} doesn't match the DataFrame height of {}\n\n\
                             If you want this Series to be broadcasted, ensure it is a scalar (for instance by adding '.first()').",
-                            c.name(), len, height
+                            c.name(), len, df_height
                         );
                     }
                 }
diff --git a/py-polars/tests/unit/dataframe/test_extend.py b/py-polars/tests/unit/dataframe/test_extend.py
index a1f4a451d627..9d4f46c95e2d 100644
--- a/py-polars/tests/unit/dataframe/test_extend.py
+++ b/py-polars/tests/unit/dataframe/test_extend.py
@@ -84,3 +84,14 @@ def test_extend_column_name_mismatch() -> None:
 
     with pytest.raises(ShapeError):
         df1.extend(df2)
+
+
+def test_initialize_df_18736() -> None:
+    # Completely empty initialization
+    df = pl.DataFrame()
+    s_0 = pl.Series([])
+    s_1 = pl.Series([None])
+    s_2 = pl.Series([None, None])
+    assert df.with_columns(s_0).shape == (0, 1)
+    assert df.with_columns(s_1).shape == (1, 1)
+    assert df.with_columns(s_2).shape == (2, 1)