diff --git a/tornado/options.py b/tornado/options.py
index 7ebae719f..917c934bd 100644
--- a/tornado/options.py
+++ b/tornado/options.py
@@ -640,6 +640,8 @@ def _parse_datetime(self, value: str) -> datetime.datetime:
     )
 
     def _parse_timedelta(self, value: str) -> datetime.timedelta:
+        if not value or not value.strip():
+            raise Error("Invalid time delta: %r" % value)
         try:
             sum = datetime.timedelta()
             start = 0
diff --git a/tornado/test/options_test.py b/tornado/test/options_test.py
index 6c76da364..ab7f4b865 100644
--- a/tornado/test/options_test.py
+++ b/tornado/test/options_test.py
@@ -5,7 +5,7 @@
 from io import StringIO
 from unittest import mock
 
-from tornado.options import Error, OptionParser
+from tornado.options import Error, OptionParser, _Option
 from tornado.util import basestring_type
 
 
@@ -261,6 +261,20 @@ def test_error_redefine(self):
             options.define("foo")
         self.assertRegex(str(cm.exception), "Option.*foo.*already defined")
 
+    def test_parse_timedelta_empty_or_whitespace_raises(self):
+        # Empty or whitespace-only timedelta values used to be silently
+        # accepted as 0 (the while loop body never ran), so `--t=` and
+        # `--t=" "` both parsed as datetime.timedelta(0). They now raise
+        # options.Error with the offending value in the message, matching
+        # the other type-specific parsers in this module.
+        for bad in ("", " ", "\t", "\n", "   \t  "):
+            option = _Option(
+                "t", type=datetime.timedelta, default=datetime.timedelta(0)
+            )
+            with self.assertRaises(Error) as cm:
+                option._parse_timedelta(bad)
+            self.assertIn(repr(bad), str(cm.exception))
+
     def test_error_redefine_underscore(self):
         # Ensure that the dash/underscore normalization doesn't
         # interfere with the redefinition error.