The following text is available in the following address: http://www.elvish.org/gwaith/calendars.htm. It is attributed to Boris Shapiro.

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The Calendar of Imladris and its adaptation for Gregorian reckoning

A short note about E.c.: as Samwise remarked, the Elves who had more time at their disposal reckoned it in longer periods. An elven 'year' - yén - actually means 144 of our years, so we better call it a century. But they also observed a 'normal' solar year - coranar or loa - of 365 days, Such a year they divided into six seasons - four of 54 and two (the second and the fifth ones) of 72 days. See Appendix D for the details. They had five days outside the months, just as the Hobbits did (but the latter did not invent them, of course), once in twelve years three days in the middle of the year - enderi - were doubled. In the last year of every third yén such doubling did not occur. One yén consisted of 52596 days. For the convenience I will use year numbers in the Gregorian reckoning (though an elven year starts approximately three months later). And remember that yestarë is the first day of the year, and with it shifts the whole year (and all the following years, until another leap-year happens - in G.c. or in E.c.).

I'd like to stress the third yén omitting of the enderi. This played a major part in my code logic.

In Appendix D Tolkien wrote that the Elves' New Year falls on the sixth day of Astron. Now we can easily get the corresponding date in the Gregorian calendar - it is March 29. But, as you know, that is a date for non-leap years.

This is controversial. The date for the beginning of the loa fluctuates due to previous leap periods and secular shifts. I assumed, however, that 29th of March is the first Gregorian equivalent day for the first day of the reckoning in my code.

In nowadays more and more of those who associate themselves with the Elves want to reckon the time in their way. But all of them came across one logical obstacle: we have no starting point. In his letter 211 Tolkien wrote about how long time ago did Barad-dûr fell: "I imagine the gap to be about 6000 years: that is we are now at the end of the Fifth Age, if the Ages were of about the same length as S.A. and T.A. But they have, I think, quickened; and I imagine we are actually at the end of the Sixth Age, or in the Seventh". So it is the Seventh Age, all right.

But the problem is deeper - from when we are to calculate leap circles. Because of the difference between leap circles in E.c. and G.c. these calendars periodically shift from one to three days relatively to each other. So for accurate calculation we must determine when did the Seventh Age actually began.

Here only the common sense can help us. We know that each Age began and ended with events of global scale which importance for the whole Middle-earth deserved starting reckoning a brand new Age. Such events were the First Sunrise, the Fall of Morgoth, and the Fall of Sauron etc. Alas, we do not know for certain what did Tolkien thought about the Seventh Age, but I will proceed from the assumption that such an even can only be the Birth of Christ.

Tolkien was a Roman catholic, and the meaning of Christmas for him cannot be overestimated. I am sure too that there will be no event of greater importance "tenn' Ambar-metta" and it deserves to call the Ages before it "the Elder Days". I am sure that Tolkien would agree.

As an atheist, I must protest. In the first place, there is no relation whatsoever between the calendar reckoning and Christmas. Also, the "birth of Christ" is obviously not a good reference, since it could be off by seven years in the best of our guess. This matter is taken into details in this site:
http://www.bibleinterp.com/opeds/why_3530.shtml

However, I think the author has a valid point in the sense that Tolkien was a catholic and it would make sense to use the catholic reckoning. So I guess it makes sense to calculate the Gregorian year 1 and start from the first March equinox of that year. Any necessity of referencing to periods before this point or after this point can be addressed by using "BCE" and "CE" rather than "BC" and "AD".

Anyway, alternative events like the end of WWII and Tolkien's birthday are no good at all.

So let's assume that the Seventh Age began 2000 years ago. That is approximately 52596*13 - 4*3 = 657432 days, where 52596 is the number of days in one yén, 13 is the number of yéni passed since 1 A.D., 3 is the number of enderi rejected from the last year of every third yén, 4 is the number of such years since 1 A.D.

In the Gregorian calendar this gives approximately January 8 of 1873: 36524*18 + (365*72 + 17) + 8 = 657432 days, where 36524 is the number of days in one Gregorian year, 17 is the number of bissextile days added in 72 Gregorian leap-years since 1 A.D.

Remember that our task an this stage was to determine current yén, so accuracy may be disregarded (to a certain extent): do not consider the fact that 1700 and 1800 were non-leap years, Earth axis' displacement, certain inaccuracy of the Elven calendar, relying entirely on the Gregorian calendar's sufficient accuracy. So, 13 yéni have passed and now we're in the 14th yén!

Now without much wisdom we can calculate that 128 years have passed since 1873. So now we're in the 129th loa of the 14th yén.

Since the first yén began on March 29 of year 1 A.D., the 14th yén began on March 29 of year 1873. This can be calculated with great accuracy: century length is equal in both calendars, in G.c. 10 days were omitted (from October 5 to October 14) in 1582 and February 29 was not added in 1700 and 1800, in total giving 12 days; in E.c. enderi were not doubled four times (in the last year of every third yén), in total giving 12 days too. It means that at the beginning of the 14th yén these two calendars (and their leap circles - at that moment) were perfectly synchronised.

That calculation is completely off!

The author is ignoring the fact that the omitted days were taken from the Julian calendar, which introduced an error of 1 day every 128 years. The Gregorian calendar was calibrated to make the 21st of March the approximate date of the vernal equinox, in the same way it happened in the Council of Nicaea in 325 CE. By 1582, the vernal equinox had moved (1582-325)/128 days = approximately 10 days backwards. So 10 days had to be dropped. The author ignores the fact that these days were counted in the previous centuries, so it doesn't mean they didn't exist in the first place.

It means that 29th of March of 1873 was in reality the 54th of Echuir / Coirë. And it makes sense, for while the elven calendar had a shift of 12 days, the Gregorian calendar simply adjusted 10 days, leaving 2 days difference.

1876 was a leap year in the Gregorian calendar, it means that February 29 was added. It means that G.c. outrunned E.c. for one day. So yestarë retarded from March 29 for one day. One more day was added in 1880 - and yestarë became two days behind. In 1884 this shift was increased for one more day, thus archieving three days. But already in 1885 (loa 12) elven leap circle was accomplished adding three more days in the middle of loa, so in 1886 (loa 13) E.c. made up for lost time, catching up with G.c. so that yestarë fell on March 29 again.*

* We need to remember that the bissextile shift occurred in the middle of the year, so all the dates after enderi fell into place immediately in that leap year, but the dates before enderi (such as yestare) did so only in the next Gregorean year. And adding the bissextile day in G.c. affected all the dates in E.c. that followed February 28 in G.c. - that is the end and of the previous an all the next elven year (and so on).

These are the periodical shifts I was talking about. It happens during each twelve-year period, that is why elven dates are not rigidly fixed in our calendar. Such shift we are to take into account in our calculations, since elven dates like yestarë admittedly fall into place only once in twelve years.

We also need to remember about, so to speak, anti-leap circles: in E.c., as we know, enderi, are not doubled in every last year of every third yén, and in G.c. February 29 is not added in century years wich are not divisible by 400 (that is in 1700, 1800, 1900, 2100 A.D. etc).

Since 1872 in G.c. elven leap years were 1884 (loa 12) , 1896 (loa 24), … 1992 (loa 120). But in 1900 in G.c. there were no 'planned' February 29, so E.c. outrunned G.c. for one day forward after three additional enderi of 1908, so the yestarë of 1909 fell on March 30…

In 1994 yestarë again fell on March 30. In 1996 (which was a leap year in G.c.) yestarë occurred one day earlier - on March 29, in 2000 and 2001 (for the same reason) - on March 28. It also can be calculated with great accuracy: before 1873, as I have said, two calendars ran evenly, from 1873 to 1993 in G.c. 365*120 + 30*1 (without February 29 of 1900) days passed and in E.c. - 365*120 + 8*4, so everything is all right, the shift amounted two days.

So on March 28 of year 2001 A.D. we entered the 129th loa of the 14th yén of the Seventh Age.

Addendum for our descendants and others

An instruction for calculating yestarë in this century: 2004 (loa 132) will be a leap year in both G.c. and E.c., that is yestarë will fall on March 27, but all the dates in E.c. after doubled enderi will be shifted forward for three days. Hence in 2005 yestare will fall on March 30, in 2008 - on March 29, and in 2012 - on March 28. 2016, which will be the last year of the 14th yén, will be a leap year in both G.c. and E.c., so the situation will be identical to 2004. And 2017 will be the first year of the 15th yén, its yestarë will fall of March 30 - these are the consequences of February 29 absent in 1900.

© 2001 by Boris Shapiro, All rights reserved