When is Bilbo and Frodo's birthday?

Whether you still look forward to celebrating your birthday or it's become a tiresome ritual reminding you of your own mortality, I bet you aren't as old as Bilbo turned in The Lord of the Rings: The Fellowship of the Ring.

You may recall that Bilbo even shares a birthday with his nephew and heir, Frodo. And despite the fact that the Shireian (i.e., the calendar of the Shire)  and Gregorian calendars do differ somewhat, this is a date they both share.

Do you remember what it is?