King’s Reckoning

The exact date of origin of the King's Reckoning is not entirely clear, but given that there was no King of Númenor until II 32, we can say for sure that, even if it existed before that date, it would not have been known as the 'King's Reckoning'.

It's stated explicitly that the King's Reckoning was 'ultimately of Eldarin origin' (The Lord of the Rings Appendix D, The Calendars), though we're given no specific detail beyond this. Presumably the calendar would have been adapted from that used by the Elves of Beleriand during the First Age. Known calendars of the Elves, such as the Reckoning of Rivendell, differ from the King's Reckoning in some significant ways, implying that either the Elves used a quite different calendar at that time, or the Dúnedain introduced substantial innovations of their own.

The Dúnedain preferred to use Sindarin terminology in their calendars, but for the individual days of the calendar like Mettarë or Yestarë we're only given Quenya versions. This might be intended to suggest that the Dúnedain used the Quenya terms for these days, or that they used some Sindarin equivalent not directly recorded. Unofficial, though commonly quoted, sources suggest Minien for Yestarë and Penninor for Mettarë.

To address the question of leap years, every fourth year the single day of the Loëndë ('year-middle') was replaced by two days collectively known as Enderi or 'middle-days'.