diff --git a/api/streaming.py b/api/streaming.py
index 9c9ea54e..03b562c7 100644
--- a/api/streaming.py
+++ b/api/streaming.py
@@ -6508,7 +6508,7 @@ def _terminal_turn_duration(session, *, now: float | None = None) -> float | Non
     try:
         started = float(started_at)
         ended = float(time.time() if now is None else now)
-    except (TypeError, ValueError):
+    except (TypeError, ValueError, OverflowError):
         return None
     if not math.isfinite(started) or not math.isfinite(ended) or started <= 0:
         return None
diff --git a/tests/test_issue3929_error_preserves_partial.py b/tests/test_issue3929_error_preserves_partial.py
index cda3931d..101c15ab 100644
--- a/tests/test_issue3929_error_preserves_partial.py
+++ b/tests/test_issue3929_error_preserves_partial.py
@@ -15,7 +15,7 @@ import api.streaming as streaming
 from api.models import Session
 
 
-@pytest.mark.parametrize("started_at", [None, 0, -1, "invalid", float("nan"), float("inf"), 101.0])
+@pytest.mark.parametrize("started_at", [None, 0, -1, "invalid", float("nan"), float("inf"), 101.0, 10**400])
 def test_terminal_turn_duration_omits_invalid_origin(started_at):
     session = types.SimpleNamespace(pending_started_at=started_at)