diff --git a/vortex-file/src/tests.rs b/vortex-file/src/tests.rs
index 6f74e583b7c..083d6bcdf6e 100644
--- a/vortex-file/src/tests.rs
+++ b/vortex-file/src/tests.rs
@@ -54,6 +54,7 @@ use vortex_array::expr::lt_eq;
 use vortex_array::expr::or;
 use vortex_array::expr::root;
 use vortex_array::expr::select;
+use vortex_array::expr::stats::Stat;
 use vortex_array::extension::datetime::TimeUnit;
 use vortex_array::extension::datetime::Timestamp;
 use vortex_array::extension::datetime::TimestampOptions;
@@ -2126,6 +2127,41 @@ async fn test_writer_with_statistics() -> VortexResult<()> {
     Ok(())
 }
 
+#[tokio::test]
+async fn file_sum_is_absent_when_a_chunk_overflows() -> VortexResult<()> {
+    let dtype = DType::Struct(
+        StructFields::from_iter([("numbers", DType::from(PType::I64))]),
+        Nullability::NonNullable,
+    );
+    let mut buf = ByteBufferMut::empty();
+    let mut writer = SESSION
+        .write_options()
+        .with_file_statistics(vec![Stat::Sum])
+        .writer(&mut buf, dtype);
+
+    // The first chunk overflows, so the file sum must not be the second chunk's sum of 2.
+    for chunk in [buffer![i64::MAX, 1], buffer![2i64]] {
+        writer
+            .push(StructArray::from_fields(&[("numbers", chunk.into_array())])?.into_array())
+            .await?;
+    }
+
+    let summary = writer.finish().await?;
+    let footer_stats = summary
+        .footer()
+        .statistics()
+        .vortex_expect("file statistics were requested");
+    assert!(footer_stats.stats_sets()[0].get(Stat::Sum).is_absent());
+
+    let file = SESSION.open_options().open_buffer(buf)?;
+    let file_stats = file
+        .file_stats()
+        .vortex_expect("file statistics were written");
+    assert!(file_stats.stats_sets()[0].get(Stat::Sum).is_absent());
+
+    Ok(())
+}
+
 #[tokio::test]
 async fn test_file_metadata_roundtrip() -> VortexResult<()> {
     let array =
diff --git a/vortex-layout/src/layouts/file_stats.rs b/vortex-layout/src/layouts/file_stats.rs
index 332012c8cd4..3d031a65c7a 100644
--- a/vortex-layout/src/layouts/file_stats.rs
+++ b/vortex-layout/src/layouts/file_stats.rs
@@ -158,6 +158,13 @@ impl StatsAccumulator {
                     // upper bound, so aggregating by skipping nulls would be unsound.
                     continue;
                 }
+                Stat::Sum if !values.all_valid(ctx)? => {
+                    // `values` holds each chunk's `Stat::Sum` from `push_chunk`. The legacy `Sum`
+                    // aggregate behind it returns zero for empty input and null only on overflow.
+                    // Summing `values` below would skip those nulls and report a wrong exact
+                    // total, so leave the file sum unset.
+                    continue;
+                }
                 Stat::Min | Stat::Max | Stat::Sum => {
                     if let Some(s) = values.statistics().compute_stat(stat, ctx)?
                         && let Some(v) = s.into_value()
@@ -531,6 +538,7 @@ mod tests {
     use vortex_array::IntoArray;
     use vortex_array::array_session;
     use vortex_array::arrays::BoolArray;
+    use vortex_array::arrays::PrimitiveArray;
     use vortex_array::arrays::bool::BoolArrayExt;
     use vortex_array::builders::VarBinViewBuilder;
     use vortex_buffer::BitBuffer;
@@ -636,4 +644,33 @@ mod tests {
             &[Stat::Max.name(), Stat::Min.name(), Stat::Sum.name()]
         );
     }
+
+    #[rstest]
+    #[case::one_chunk_overflows(vec![vec![Some(i64::MAX), Some(1)], vec![Some(2)]], None)]
+    #[case::all_chunks_overflow(vec![vec![Some(i64::MAX), Some(1)]; 2], None)]
+    #[case::total_overflows(vec![vec![Some(i64::MAX)], vec![Some(1)]], None)]
+    #[case::nullable_values(vec![vec![None, Some(3)], vec![Some(4), None]], Some(7))]
+    #[case::all_null_chunk(vec![vec![None], vec![Some(5)]], Some(5))]
+    fn combines_chunk_sums(
+        #[case] chunks: Vec<Vec<Option<i64>>>,
+        #[case] expected: Option<i64>,
+    ) -> VortexResult<()> {
+        let mut ctx = array_session().create_execution_ctx();
+        let dtype = DType::Primitive(PType::I64, Nullability::Nullable);
+        let mut acc = StatsAccumulator::new(&dtype, &[Stat::Sum], 12);
+        for chunk in chunks {
+            acc.push_chunk(
+                &PrimitiveArray::from_option_iter(chunk).into_array(),
+                &mut ctx,
+            )?;
+        }
+
+        let stats = acc.as_stats_set(&[Stat::Sum], &mut ctx)?;
+        assert_eq!(
+            stats.get(Stat::Sum),
+            expected.map_or(Precision::Absent, Precision::exact)
+        );
+
+        Ok(())
+    }
 }