diff --git a/CHANGELOG.md b/CHANGELOG.md
index 99f5c06e413..b74f8e97721 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -115,6 +115,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed corner case for `PearsonCorrCoef` when running in ddp mode but only on single device ([#1587](https://github.com/Lightning-AI/metrics/pull/1587))
 
 
+- Fixed overflow error for specific cases in `MAP` when big areas are calculated ([#1607](https://github.com/Lightning-AI/metrics/pull/1607))
+
+
 ## [0.11.2] - 2023-02-21
 
 ### Fixed
diff --git a/src/torchmetrics/detection/mean_ap.py b/src/torchmetrics/detection/mean_ap.py
index ff9ace379f2..732342d6b69 100644
--- a/src/torchmetrics/detection/mean_ap.py
+++ b/src/torchmetrics/detection/mean_ap.py
@@ -392,10 +392,10 @@ def __init__(
             raise ModuleNotFoundError("When `iou_type` is set to 'segm', pycocotools need to be installed")
         self.iou_type = iou_type
         self.bbox_area_ranges = {
-            "all": (0**2, int(1e5**2)),
-            "small": (0**2, 32**2),
-            "medium": (32**2, 96**2),
-            "large": (96**2, int(1e5**2)),
+            "all": (float(0**2), float(1e5**2)),
+            "small": (float(0**2), float(32**2)),
+            "medium": (float(32**2), float(96**2)),
+            "large": (float(96**2), float(1e5**2)),
         }
 
         if not isinstance(class_metrics, bool):