diff --git a/backend/app/engine/recompute.py b/backend/app/engine/recompute.py
index bf2bc524..8636d24e 100644
--- a/backend/app/engine/recompute.py
+++ b/backend/app/engine/recompute.py
@@ -473,6 +473,9 @@ def _compute(plan: _Plan, values: dict[str, Any], notes: dict[str, list[int]],
         if inp.row is not None and path in notes and path not in changes.inputs:
             return "excluded", None, f"{EXCLUDED}：{path} 所在的第 {inp.row + 1} 行已排除"
     value, reason = _evaluate(plan, values)
+    if reason is None and isinstance(value, float) and not math.isfinite(value):
+        # 溢出成无穷大、算出非数：口径卡渲染成「—」，这里也说清算不出来（JSON 里也放不下这种值）
+        reason = "计算结果不是有限的数值（溢出或非数），无法推演"
     return ("ok", value, None) if reason is None else ("error", None, reason)
 
 
@@ -545,7 +548,7 @@ def _result(plan: _Plan, status: str, new: Any, reason: str | None, values: dict
     return {
         "id": metric.get("id"), "name": metric.get("name") or metric.get("id"), "unit": metric.get("unit") or "",
         "decimals": metric.get("decimals"), "format": metric.get("format") or DEFAULT_FORMAT,
-        "old": old, "new": new, "delta": delta,
+        "old": _finite(old), "new": _finite(new), "delta": delta,
         "rendered_old": _render(metric, old), "rendered_new": _render(metric, new) if known else None,
         "rendered_delta": rendered_delta,
         "changed": (not _same(old, new)) if known else None,
@@ -562,6 +565,11 @@ def _render(metric: dict[str, Any], value: Any, conv: str | None = None) -> str:
         return MISSING
 
 
+def _finite(value: Any) -> Any:
+    """无穷大、非数换成 None：老卡上可能记着（口径卡渲染成「—」），JSON 里放不下。"""
+    return None if isinstance(value, float) and not math.isfinite(value) else value
+
+
 def _same(a: Any, b: Any) -> bool:
     if is_number(a) and is_number(b):
         return a == b or (isinstance(a, float) and isinstance(b, float) and math.isnan(a) and math.isnan(b))
@@ -620,7 +628,7 @@ def _input_view(inp: _Input, values: dict[str, Any], notes: dict[str, list[int]]
         new = _outline(values.get(inp.path), inp.table) if inp.problem is None else None
         changed = inp.problem is None and not _same(old, new)
     else:
-        old, new = item.get("value"), values.get(inp.path)
+        old, new = _finite(item.get("value")), _finite(values.get(inp.path))
         changed = not _same(old, new)
     view.update(old=old, new=new, changed=changed)
     if inp.path in notes:
diff --git a/backend/tests/test_recompute.py b/backend/tests/test_recompute.py
index 83081459..1b9b6594 100644
--- a/backend/tests/test_recompute.py
+++ b/backend/tests/test_recompute.py
@@ -218,6 +218,21 @@ def test_division_by_zero_is_explained():
     assert wow["status"] == "error" and wow["new"] is None and wow["reason"] == "除以零"
 
 
+def test_an_overflow_is_an_error_not_a_crash():
+    """算出无穷大：说清算不出来；老卡上记着无穷大的也不往外送（JSON 放不下，接口会 500）。"""
+    import json
+
+    result = whatif(CARD, Changes(inputs={"vars.kpi.refunds": 1e308, "vars.kpi.orders": 1e-10}), sources(),
+                    metric="ratio")
+    [ratio] = result["metrics"]
+    assert ratio["status"] == "error" and ratio["new"] is None and "有限" in ratio["reason"]
+    card = {**CARD, "metrics": [metric("big", "vars.kpi.x * 2", "inf * 2", math.inf,
+                                       [scalar("vars.kpi.x", math.inf)], rendered="—")]}
+    big = whatif(card, Changes(), sources())["metrics"][0]
+    assert big["old"] is None and big["inputs"][0]["old"] is None and big["rendered_old"] == "—"
+    json.dumps([result, big], allow_nan=False)
+
+
 def test_a_missing_input_can_be_supplied():
     card = {**CARD, "metrics": [metric("cost", "vars.kpi.cost / vars.kpi.orders", "vars.kpi.cost / 1234", None,
                                        [scalar("vars.kpi.cost", None), scalar("vars.kpi.orders", 1234)], decimals=2,