diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -178,7 +178,8 @@
             n = -(256 ** (len(s) - 1) - n)
     else:
         try:
-            n = int(nts(s, "ascii", "strict") or "0", 8)
+            s = nts(s, "ascii", "strict")
+            n = int(s.strip() or "0", 8)
         except ValueError:
             raise InvalidHeaderError("invalid header")
     return n
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1842,6 +1842,10 @@
         self.assertEqual(tarfile.nti(b"\xff\x00\x00\x00\x00\x00\x00\x00"),
                          -0x100000000000000)
 
+        # Issue 24514: Test if empty number fields are converted to zero.
+        self.assertEqual(tarfile.nti(b"\0"), 0)
+        self.assertEqual(tarfile.nti(b"       \0"), 0)
+
     def test_write_number_fields(self):
         self.assertEqual(tarfile.itn(1), b"0000001\x00")
         self.assertEqual(tarfile.itn(0o7777777), b"7777777\x00")