What is the largest Safe UDP Packet Size on the Internet

It is true that a typical IPv4 header is 20 bytes, and the UDP header is 8 bytes. However it is possible to include IP options which can increase the size of the IP header to as much as 60 bytes. In addition, sometimes it is necessary for intermediate nodes to encapsulate datagrams inside of another protocol such as IPsec (used for VPNs and the like) in order to route the packet to its destination. So if you do not know the MTU on your particular network path, it is best to leave a reasonable margin for other header information that you may not have anticipated. A 512-byte UDP payload is generally considered to do that, although even that does not leave quite enough space for a maximum size IP header.

The maximum safe UDP payload is 508 bytes. This is a packet size of 576 (the "minimum maximum reassembly buffer size"), minus the maximum 60-byte IP header and the 8-byte UDP header.

Any UDP payload this size or smaller is guaranteed to be deliverable over IP (though not guaranteed to be delivered). Anything larger is allowed to be outright dropped by any router for any reason. Except on an IPv6-only route, where the maximum payload is 1,212 bytes. As others have mentioned, additional protocol headers could be added in some circumstances. A more conservative value of around 300-400 bytes may be preferred instead.

The maximum possible UDP payload is 67 KB, split into 45 IP packets, adding an additional 900 bytes of overhead (IPv4, MTU 1500, minimal 20-byte IP headers).

Any UDP packet may be fragmented. But this isn't too important, because losing a fragment has the same effect as losing an unfragmented packet: the entire packet is dropped. With UDP, this is going to happen either way.

^{_{IP packets include a fragment offset field, which indicates the byte offset of the UDP fragment in relation to its UDP packet. This field is 13-bit, allowing 8,192 values, which are in 8-byte units. So the range of such offsets an IP packet can refer to is 0...65,528 bytes. Being an offset, we add 1,480 for the last UDP fragment to get 67,008. Minus the UDP header in the first fragment gives us a nice, round 67 KB.}}

Sources: RFC 791, RFC 1122, RFC 2460

The theoretical limit (on Windows) for the maximum size of a UDP packet is 65507 bytes. This is documented here:

The correct maximum UDP message size is 65507, as determined by the following formula: 0xffff - (sizeof(IP Header) + sizeof(UDP Header)) = 65535-(20+8) = 65507

That being said, most protocols limit to a much smaller size - usually either 512 or occasionally 8192. You can often go higher than 548 safely if you are on a reliable network - but if you're broadcasting across the internet at large, the larger you go, the more likely you'll be to run into packet transmission problems and loss.

576 is the minimum maximum reassembly buffer size, i.e. each implementation must be able to reassemble packets of at least that size. See IETF RFC 1122 for details.