diff --git a/crates/polars-core/src/series/implementations/null.rs b/crates/polars-core/src/series/implementations/null.rs
index b0e4a7d6e26a..b5d32aab0f8d 100644
--- a/crates/polars-core/src/series/implementations/null.rs
+++ b/crates/polars-core/src/series/implementations/null.rs
@@ -81,6 +81,23 @@ impl PrivateSeries for NullChunked {
         ExplodeByOffsets::explode_by_offsets(self, offsets)
     }
 
+    fn subtract(&self, _rhs: &Series) -> PolarsResult<Series> {
+        null_arithmetic(self, _rhs, "subtract")
+    }
+
+    fn add_to(&self, _rhs: &Series) -> PolarsResult<Series> {
+        null_arithmetic(self, _rhs, "add_to")
+    }
+    fn multiply(&self, _rhs: &Series) -> PolarsResult<Series> {
+        null_arithmetic(self, _rhs, "multiply")
+    }
+    fn divide(&self, _rhs: &Series) -> PolarsResult<Series> {
+        null_arithmetic(self, _rhs, "divide")
+    }
+    fn remainder(&self, _rhs: &Series) -> PolarsResult<Series> {
+        null_arithmetic(self, _rhs, "remainder")
+    }
+
     #[cfg(feature = "algorithm_group_by")]
     fn group_tuples(&self, _multithreaded: bool, _sorted: bool) -> PolarsResult<GroupsProxy> {
         Ok(if self.is_empty() {
@@ -98,6 +115,16 @@ impl PrivateSeries for NullChunked {
     }
 }
 
+fn null_arithmetic(lhs: &NullChunked, rhs: &Series, op: &str) -> PolarsResult<Series> {
+    let output_len = match (lhs.len(), rhs.len()) {
+        (1, len_r) => len_r,
+        (len_l, 1) => len_l,
+        (len_l, len_r) if len_l == len_r => len_l,
+        _ => polars_bail!(ComputeError: "Cannot {:?} two series of different lengths.", op),
+    };
+    Ok(NullChunked::new(lhs.name().into(), output_len).into_series())
+}
+
 impl SeriesTrait for NullChunked {
     fn name(&self) -> &str {
         self.name.as_ref()
diff --git a/py-polars/tests/unit/operations/arithmetic/test_arithmetic.py b/py-polars/tests/unit/operations/arithmetic/test_arithmetic.py
index 317cf68ffba1..15d4f865576b 100644
--- a/py-polars/tests/unit/operations/arithmetic/test_arithmetic.py
+++ b/py-polars/tests/unit/operations/arithmetic/test_arithmetic.py
@@ -270,3 +270,26 @@ def test_operator_arithmetic_with_nulls(op: Any) -> None:
 
         assert_frame_equal(df_expected, op(df, None))
         assert_series_equal(s_expected, op(s, None))
+
+
+@pytest.mark.parametrize(
+    "op",
+    [
+        operator.add,
+        operator.mod,
+        operator.mul,
+        operator.sub,
+    ],
+)
+def test_null_column_arithmetic(op: Any) -> None:
+    df = pl.DataFrame({"a": [None, None], "b": [None, None]})
+    expected_df = pl.DataFrame({"a": [None, None]})
+
+    output_df = df.select(op(pl.col("a"), pl.col("b")))
+    assert_frame_equal(expected_df, output_df)
+    # test broadcast right
+    output_df = df.select(op(pl.col("a"), pl.Series([None])))
+    assert_frame_equal(expected_df, output_df)
+    # test broadcast left
+    output_df = df.select(op(pl.Series("a", [None]), pl.col("a")))
+    assert_frame_equal(expected_df, output_df)