diff --git a/src/anthropic/_base_client.py b/src/anthropic/_base_client.py
index 4cba75e9..41365644 100644
--- a/src/anthropic/_base_client.py
+++ b/src/anthropic/_base_client.py
@@ -690,7 +690,8 @@ def _calculate_retry_timeout(
         if retry_after is not None and 0 < retry_after <= 60:
             return retry_after
 
-        nb_retries = max_retries - remaining_retries
+        # Also cap retry count to 1000 to avoid any potential overflows with `pow`
+        nb_retries = min(max_retries - remaining_retries, 1000)
 
         # Apply exponential backoff, but not more than the max.
         sleep_seconds = min(INITIAL_RETRY_DELAY * pow(2.0, nb_retries), MAX_RETRY_DELAY)
diff --git a/tests/test_client.py b/tests/test_client.py
index 73d296a7..85805101 100644
--- a/tests/test_client.py
+++ b/tests/test_client.py
@@ -804,6 +804,7 @@ class Model(BaseModel):
             [3, "", 0.5],
             [2, "", 0.5 * 2.0],
             [1, "", 0.5 * 4.0],
+            [-1100, "", 7.8],  # test large number potentially overflowing
         ],
     )
     @mock.patch("time.time", mock.MagicMock(return_value=1696004797))
@@ -1768,6 +1769,7 @@ class Model(BaseModel):
             [3, "", 0.5],
             [2, "", 0.5 * 2.0],
             [1, "", 0.5 * 4.0],
+            [-1100, "", 7.8],  # test large number potentially overflowing
         ],
     )
     @mock.patch("time.time", mock.MagicMock(return_value=1696004797))