When was Bilbo and Frodo's Birthday?
From: The Tolkien FAQ by William D.B. Loos
The date on the Shire calendar was September 22 (The Fellowship of the Ring, 29). Both the different definitions of the months and the different correlation of their calendar with the seasons (the summer solstice fell on Mid-year's Day, the day between June and July, not on June 21 as on our calendar (The Return of the King, 388 - Appendix D)) must be taken into account. The discrepancy in September is found to be 10 days, giving September 12 on our calendar as the equivalent date. (This result has some significance for the story. Events occur ten days earlier in terms of the seasons than the dates would suggest to us: when sleeping outdoors in autumn, ten days can make a large difference.)
(In Appendix D Tolkien gives detailed information about long-term inaccuracies in the Shire Reckoning, which they dealt with differently than we do. Based on this, it is possible to conclude that the SR at the time of the story had accumulated either two days or four days of error, depending on how careful the Hobbits were about making long term corrections, which we aren't told. This result would make the equivalent date either September 14 or September 16, but other considerations raise questions about the accuracy of such calculations, so September 12 is probably the most straightforward choice.)
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