diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 082f361..d7c1500 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -186,7 +186,7 @@
     # itn() below.
     if s[0] != chr(0200):
         try:
-            n = int(nts(s) or "0", 8)
+            n = int(nts(s).strip() or "0", 8)
         except ValueError:
             raise InvalidHeaderError("invalid header")
     else:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index ff3265f..a92d371 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1566,6 +1566,14 @@
         tarinfo.tobuf(tarfile.PAX_FORMAT)
 
 
+class MiscTest(unittest.TestCase):
+
+    def test_read_number_fields(self):
+        # Issue 24514: Test if empty number fields are converted to zero.
+        self.assertEqual(tarfile.nti("\0"), 0)
+        self.assertEqual(tarfile.nti("       \0"), 0)
+
+
 class ContextManagerTest(unittest.TestCase):
 
     def test_basic(self):
@@ -1730,6 +1738,7 @@
         PaxUnicodeTest,
         AppendTest,
         LimitsTest,
+        MiscTest,
         ContextManagerTest,
     ]
 
diff --git a/Misc/NEWS b/Misc/NEWS
index e6240e2..e46b701 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -34,6 +34,9 @@
 Library
 -------
 
+- Issue #24514: tarfile now tolerates number fields consisting of only
+  whitespace.
+
 - Issue #20387: Restore semantic round-trip correctness in tokenize/untokenize
   for tab-indented blocks.