diff --git a/jsonschema/_format.py b/jsonschema/_format.py
index 62c0e4ee..2ed23454 100644
--- a/jsonschema/_format.py
+++ b/jsonschema/_format.py
@@ -3,6 +3,7 @@
 from contextlib import suppress
 from datetime import date, datetime
 from uuid import UUID
+import decimal
 import ipaddress
 import re
 import string
@@ -518,7 +519,7 @@ def is_uri_template(instance: object) -> bool:
     @_checks_drafts(
         draft201909="duration",
         draft202012="duration",
-        raises=isoduration.DurationParsingException,
+        raises=(isoduration.DurationParsingException, decimal.Overflow),
     )
     def is_duration(instance: object) -> bool:
         if not isinstance(instance, str):
diff --git a/jsonschema/tests/test_format.py b/jsonschema/tests/test_format.py
index d829f984..ed777641 100644
--- a/jsonschema/tests/test_format.py
+++ b/jsonschema/tests/test_format.py
@@ -2,12 +2,17 @@
 Tests for the parts of jsonschema related to the :kw:`format` keyword.
 """
 
-from unittest import TestCase
+from unittest import TestCase, skipUnless
 
 from jsonschema import FormatChecker, ValidationError
 from jsonschema.exceptions import FormatError
 from jsonschema.validators import Draft4Validator
 
+try:
+    import isoduration
+except ImportError:
+    isoduration = None
+
 BOOM = ValueError("Boom!")
 BANG = ZeroDivisionError("Bang!")
 
@@ -80,6 +85,24 @@ def test_format_checkers_come_with_defaults(self):
         with self.assertRaises(FormatError):
             checker.check(instance="not-an-ipv4", format="ipv4")
 
+    @skipUnless(isoduration is not None, "isoduration not installed")
+    def test_duration_with_a_huge_exponent_is_invalid_not_an_error(self):
+        # A duration amount whose magnitude exceeds the decimal context's
+        # ``Emax`` makes isoduration's ``Decimal(...)`` raise
+        # ``decimal.Overflow`` rather than ``DurationParsingException``.  Such
+        # a string is not a valid RFC 3339 Appendix A duration and should be
+        # reported as invalid, not propagate an uncaught exception.
+        checker = FormatChecker()
+        with self.assertRaises(FormatError):
+            checker.check(instance="P1E1000000D", format="duration")
+
+    @skipUnless(isoduration is not None, "isoduration not installed")
+    def test_duration_with_a_huge_digit_run_is_invalid_not_an_error(self):
+        checker = FormatChecker()
+        instance = "P" + "1" * 1000001 + "D"
+        with self.assertRaises(FormatError):
+            checker.check(instance=instance, format="duration")
+
     def test_repr(self):
         checker = FormatChecker(formats=())
         checker.checks("foo")(lambda thing: True)  # pragma: no cover