A Simulation of J.R.R. Tolkien’s Calendars throughout Middle-earth’s History


The primary goal of the default calendars on this project’s home page is to visualize how the calendars described in J.R.R. Tolkien’s The Lord of the Rings Appendix D relate to our modern day Gregorian calendar. Those are the calendars one would use if they were only interested in a Shire, Gondor, or Rivendell date conversion for today’s date in modern times. For example, if you simply want to know how a Shire date listed on Tolkien Gateway would convert into a date in this year’s calendar, use the default Shire Calendar on this project’s home page.

As pointed out in the Shire Reckoning notes, the calendars of Gondor and the Shire described in Appendix D had similar yet different leap-year and leap-day rules compared to our Gregorian calendar. So this project also includes a way to reckon Shire and Gondor dates according to the “traditional” leap-day and leap-year rules as described in Appendix D. This allows me to implement a simulation that can display these calendars according to Shire-reckoning years and the Ages of Middle-earth.

If you’re more interested in how these different leap-day rules of Appendix D cause dates to shift in each of these calendars relative to each other, or how these calendar rules would shift dates relative to the Gregorian calendar over thousands of years, or if you’re only interested in how the Middle-earth calendars related to each other around the War of the Ring, then you may be more interested in these Middle-earth calendar simulations.

I’m confident I have carefully reproduced all of the rules of Appendix D in these simulations as accurately as possible, given the information available in the Appendices, and my analysis of Tolkien’s Deficit calculations should support this.

Various ways of synchronizing Gregorian years with Shire-reckoning years and the Ages of Middle-earth are also provided by the live demonstration below.

How to Use these Calendar Simulations

  1. Choose a Synchronize setting to align Middle-earth years and dates with Gregorian dates.
  2. Choose one of the events of Middle-earth in the Dates of Interest list to see its corresponding date in each calendar, as well as which Gregorian date corresponds to that chosen event, for the selected Synchronize scheme.
    • These dates are listed in descending order, from latest to earliest.
    • Months and days are given according to Shire Reckoning, except for a few dates before Bilbo’s time, which are given according to the Stewards’ or Kings’ Reckoning.
  3. Adjusting the Shire-reckoning or Gregorian Date will change the date displayed in each calendar, and may update the selected event in the Dates of Interest list, depending on the date or year of the event.
  4. Adjusting the Time of Day will adjust the date in the Gondor or Rivendell calendar, due to the way they reckon the start or end of a day.
    • Adjusting the selected Dates of Interest or the Gregorian date will reset the Time of Day to Daytime, to help avoid confusion about which Gondor or Rivendell date corresponds to the selected event or Gregorian date.
    • Keep in mind that the Gregorian date labels in those calendars are meant to be the corresponding date during the daytime on those days.
    • See the notes below for more details and an example of how the Gondor and Rivendell calendars reckon the start or end of a day.
  5. Adjusting the Start reckoning from Gregorian dates in any of the calendars will update the Synchronize setting to a Custom Reckoning setting.
    • The events of Middle-earth in the Dates of Interest list are tied to this simulation’s Shire Reckoning calendar, so adjusting the Shire Reckoning’s starting Gregorian date will also adjust those events’ corresponding Gregorian dates. Also, in order to keep the Shire and Gondor calendars in sync, adjusting the Start reckoning from Gregorian date of one will also set it to that Gregorian date in the other. The Start reckoning from Gregorian dates in the Shire and Gondor calendars correspond to the first year of the Second Age.
    • Since the Appendices only mentioned the one Rivendell calendar date (New Year’s Day) that corresponded to a Shire calendar date (Third Age 3019 Astron 6), this simulation’s Rivendell Reckoning Start reckoning from Gregorian date can be adjusted without affecting the other calendars. As a result, the Dates of Interest event “III 3019 Astron 6” may no longer correspond to Rivendell’s New Year’s Day, depending on the custom adjustments to the Shire and Rivendell Start reckoning from Gregorian dates.
  6. See my Shire Reckoning notes for more details about the names and layout of the days, weeks, and months of the Shire Calendar.

Caveats and Minutiae

What’s Considered Canon in these Simulations?

Tolkien gave us just enough details about these calendar systems in Appendix D to make these simulations possible, but he didn’t give us enough details to let us know how accurate these simulations might be throughout the history of Middle-earth. I know some readers would like to know in which years these calendars are accurate enough to be considered canon according to Tolkien’s Legendarium, so I will do my best in this section to summarize what could be considered canon, and in the following sections I will explain how I had to fill in the gaps with my own estimations to make these simulations possible.

Note that when giving Middle-earth years throughout the rest of these notes, I will use S.R. = Shire-reckoning, IV = Fourth Age, III = Third Age, II = Second Age, and Iys = First Age Years of the Sun.

First some Caveats

I want to emphasize that none of the corresponding Gregorian dates in any of the synchronization schemes can be considered canon. Tolkien never firmly fixed these stories to a specific period in our actual history. He included a rough estimate in his letter #211 that the events of The Lord of the Rings could have occurred around 6000 years ago, but in one note published in The Nature of Middle-earth, he speculates that Iys 310 could have occurred 16000 years ago, putting the events of The Lord of the Rings further back to around 9000 years ago. So these simulations provide many possible synchronization schemes.

These simulations also make no attempt to display these calendars with the appropriate language during any given year. For example, the Hobbits used more archaic names for their months and weekdays around “nine hundred years before Frodo’s time”, which by the time of the War of the Ring (and we are not told exactly when), became the Shire Reckoning names displayed by these simulations. Also note how the month names used for the “Disaster of the Gladden Fields” in Unfinished Tales were given in Sindarin (III 2 Narbeleth), but the Quenya month names were used for the “Battle of the Field of Celebrant” (III 2510 Víressë). I’m also not 100% certain about some of the English translations for Quenya and Sindarin month names of the Gondor calendars, which were compiled from online sources, since Tolkien did not provide English translations of these month names in Appendix D.

So it would be unwise to assume that these simulations display every calendar exactly how they were observed by these cultures in every year of Middle-earth’s history; but one way to view these simulations, if you ignore the corresponding Gregorian dates, would be to consider them as how a Fourth Age historian might compare or convert Middle-earth dates between these different calendars, for certain events in the previous ages of Middle-earth.

In this section of the notes, I’m attempting to address questions like the following:

Now the Minutiae

The following details given in The Lord of the Rings Appendices are what I will use to determine what’s considered canon (some are also examined in my Shire Reckoning Notes and in my Rivendell Reckoning Notes):

What I Consider Canon in these Simulations

So based on those details provided by Tolkien in The Lord of the Rings Appendices, I would consider the following details as canon in this project’s simulations:

If it was considered canon that the Calendar of Imladris started its reckoning from the first Year of the Sun in the First Age, then all the dates and corresponding weekdays of this Calendar of Imladris simulation could be considered canon as well, since it follows all the rules exactly as described in Appendix D. I’ll also point out that, since Rivendell’s Yestarë must fall on Astron 6 in S.R. 1419 (III 3019), then if the Calendar of Imladris started reckoning from the first Year of the Sun, its Yestarë would also have fallen on Astron 5, 6, or 7 (or the 4th, but only in a Rivendell leap-year) from about S.R. 1400 (III 3000) until about S.R. 1500 (IV 80). So around the end of the Third Age, this appears to fit nicely with Tolkien’s statement that Rivendell’s Yestarë “corresponded more or less with Shire April 6” (Astron 6). See the notes on How the Calendar of Imladris drifts apart from the Shire Calendar for more details on how this works out.

In any case, outside of the one canon year described above, the Calendar of Imladris in these simulations should still be accurate to within 3 days when compared to the dates of the Gondor calendar in the Second and Third Ages, and when compared to the dates of the Shire Calendar around the end of the Third Age.

Reckoning the start or end of a day

Even when we know a date in all 3 calendars can be considered canon for that day, those calendar dates displayed in this simulation will only match up that way during the daylight hours of that day by default; because Tolkien stated in Appendix D that the Gondor calendars reckoned their dates from sunrise to sunrise, the Elves reckoned their dates from sunset to sunset, and it’s implied that the Hobbits reckoned their dates from midnight to midnight (as we do in modern times), exemplified in the following passage from the “Minas Tirith” chapter in The Return of the King:

With that Gandalf went out; and as he did so, there came the note of a clear sweet bell ringing in a tower of the citadel. Three strokes it rang, like silver in the air, and ceased: the third hour from the rising of the sun. After a minute Pippin went to the door and down the stair… ‘Nine o’clock we’d call it in the Shire,’ said Pippin aloud to himself.

For example, Appendix B tells us that the date the camp under Weathertop was attacked and Frodo was wounded by the Witch-king was S.R. 1418 (III 3018) Winterfilth 6. From the story we know that Strider and the hobbits arrived at Weathertop during the day, the attack happened at night, and Strider attempted to treat Frodo’s wound with Kingsfoil just before sunrise. Selecting that event from the Dates of Interest will display Winterfilth 6 in the Shire Calendar, Narquelië 6 in the Stewards’ Reckoning of Gondor, and the last Enderë of the year in the Calendar of Imladris, which is how these dates matched up during the daytime when they reached Weathertop on that day. Since the Elves reckon the next date after sunset, then when Frodo was wounded it was already considered the next day, the 1st day of Quellë, in the Calendar of Imladris. Since Strider came back with Kingsfoil after midnight but before sunrise, then it was already Winterfilth 7 by Shire Reckoning but it was still considered Narquelië 6 by the Stewards’ Reckoning in Gondor.

Shire, Gondor, and Rivendell Reckoning years

The top of each calendar displays a year appropriate to each reckoning, relative to the chosen settings described above. These years include the year 0 and can go into negative numbers. So when a date is selected during Third Age 1600, the Shire Reckoning calendar will display as year 0, and when a date is selected before the start of the Second Age both the Shire Reckoning and Gondor/Númenor calendars will display a negative year. If a calendar is displayed with a year that is negative or 0, it should be considered proleptic for that year. Similarly, the Start reckoning from dates also include the Gregorian year 0, which is equivalent to 1 B.C. (and -999 is equivalent to 1000 B.C.)

Gondor Week Days

Tolkien stated in Appendix D that “all the days, months, and dates are in the Red Book translated into Shire terms, or equated with them in notes”. This means there probably aren’t any references to a current weekday of the Gondor Calendar during the narrative of The Lord of the Rings. Tolkien also stated that the Kings’ Reckoning “was ultimately of Eldarin origin” and had a 6-day week like the Elvish calendar of the Eldar, but at some point the Númenóreans added a 7th weekday called “Sea-day” (Eärenya/Oraearon); although it’s not stated when the 7th weekday was added (one possibility may be sometime during II 883 - 1075 under the reign of Tar-Aldarion).

Appendix D also states that “in Númenor calculation started with S.A. 1”, and though this is mainly a reference to the calculation of leap-days, it may also apply to the calculation of weekdays. So for these simulations I assume that the weekdays were reckoned continuously starting with Elenya on the first day of the Second Age (Yestarë of S.A. 1). Conveniently (and perhaps intentionally by Tolkien), reckoning the weekdays of Gondor’s calendars in this manner allows them to sync up with the Shire Calendar’s weekdays during the events of the narrative, in the 2nd half of III 3018 and the 1st half of III 3019 (a.k.a. the “Great Years” of the War of the Ring).

Synchronize settings

These Gregorian Synchronize settings (except for Custom Reckonings) are configured so that all of the dates of the Shire, Gondor, and Rivendell calendars will always remain in sync with each other (and each Middle-earth calendar will still follow its own “traditional” leap-year rules), no matter which of these Synchronize settings is selected. So changing the Synchronize setting is only changing the relationship of the Gregorian calendar to these Middle-earth calendars, but not the relationship of the Middle-earth calendars to each other.

Gregorian years with Second Age years

This synchronization scheme is the one I think was most likely used by Tolkien while working out the details of The Lord of the Rings Appendix D, which I think is supported by the arguments in my Rivendell Reckoning notes, but note the following caveats:

  1. I’m not arguing that somehow the Second Age of Middle-earth was supposed to start in our actual historical year 1 A.D. I just think that Tolkien used this synchronization scheme as a “model”, or aligned a hypothetical Gregorian calendar as a kind of “measuring stick” to the start of the Second Age, when working out the details of the Gondor leap-days (or intercalations) and the Elves’ New Year’s Day of III 3019.
  2. In my notes on the First Day of the Calendar of Imladris, I point out that starting the reckoning of the Calendar of Imladris in this Gregorian calendar’s year 590 B.C.E. (-589) means that the leap-years of this Calendar of Imladris are not in sync with the leap-years of this Gregorian calendar, so comparing the dates in the Calendar of Imladris to the dates of this Gregorian calendar is a bit more complicated than the comparison of dates in the default calendar on this project’s home page. As another example of how complicated these comparisons can be, depending on how you align the Gregorian calendar “measuring stick” to these Middle-earth calendars, notice what happens to the start dates of these simulated calendars when you select the Synchronize setting for Venerable Bede’s Reckoning: the Shire and Gondor calendars will still start from a December 23 in the Gregorian year -10413, but the Rivendell Calendar will now start on a March 21 in the Gregorian year -11002, and yet Shire Astron 6 and Rivendell’s Yestarë still fall on a March 25 in the Third Age 3019!

Moon phases

These schemes attempt to align the dates of the ‘Great Years’ of the War of the Ring as much as possible with the real-world moon phases of various real-world years. See my Shire Reckoning notes for an explanation of how Tolkien used the moon phases of 1941-42 as the model for the moon phases in The Lord of the Rings. Also see Shire-Reckoning.com’s Moon Phases in The Lord of the Rings for additional details.

In 2017-18, I attempted to re-read The Lord of the Rings in chronological order, and also aligned with the moon phases in those years. It actually was not too difficult with the help of The Lord of the Rings Appendix B, the Reader’s Companion, and these calendar simulations.

I’ve collected the breakdown of each date’s reading by page number, including snippets of passages from the story where each date begins or ends, and some of my own real-world observations of the moon phases on certain dates. You can view the results and the “Grand Scheme” on the The Lord of the Rings Lunar Readalong page.

Gregorian years with Years of the Sun

The default Rivendell calendar on this project’s home page starts reckoning its first year on 1 A.D. of the proleptic Gregorian calendar in order to keep these calendars’ leap-year cycles in sync, making it easier to compare these calendar systems with each other. The next proleptic Gregorian year before 1 A.D. that starts both a Gregorian 400-year cycle and a Calendar of Imladris 432-year cycle would be 10800 B.C. since it’s evenly divisible by both 400 and 432. So this synchronization scheme starts reckoning the Calendar of Imladris from 10800 B.C., and the 7049 years from then to III 3019 would be 3751 B.C., which is fairly close to Tolkien’s 6000-year gap to our time. Interestingly, this scheme also happens to allow Rivendell’s Yestarë to fall on a proleptic Gregorian March 27 in 1 A.D. Since these calendars’ leap-year cycles are in sync in this scheme, and they both would begin a new cycle in 1 A.D., this is nearly equivalent to Boris Shapiro’s calculations which start reckoning from the proleptic Gregorian March 27 in 1 A.D. as well. The only difference would be that the first Yestarë would logically be reckoned on the first day of the week, Elenya, but reckoning the first Yestarë from on an Elenya in 10800 B.C. means the Yestarë in 1 A.D. would fall in the middle of the week, on Aldúya. So perhaps this scheme demonstrates that if we want to align the Calendar of Imladris with the Gregorian calendar, then Shapiro’s calculations can be viewed as “traditionally appropriate”, since it aligns with a Calendar of Imladris that starts its reckoning from a “seasonally appropriate” March 21 and very close to a “traditionally appropriate” year.

Venerable Bede’s Reckoning

This synchronization scheme is based on Venerable Bede’s calculation of 3952 B.C. as the year of the “creation” of the world, and aligns the first year of the Fourth Age with this year. Since Tolkien based the names of the Shire Calendar on the Anglo-Saxon calendar described in Venerable Bede’s On the Reckoning of Time (De temporum ratione), I’m guessing that he may have had Bede’s year of 3952 B.C. in mind when he estimated the events of The Lord of the Rings could have occurred around 6000 years ago in his letter #211.

James “the Just” Strom’s Reckoning

This synchronization scheme is based on the Stellarium calculations in the forum post Middle-earth chronology by “James the Just”, which aligns Mid-year’s Day in III 3019 with June 20 in 4008 B.C. This scheme also appears to match the calculations in his Imladris calendar post in the same forums.

Joe Bartram’s Reckoning

This synchronization scheme is based on this post by Joe Bartram of the Oxford Tolkien Society, Taruithorn. The Start reckoning from dates were chosen to align the start of the Shire Calendar in 2015 (S.R. 8077) with the calendar linked in part 4 of Bartram’s calendar posts.

My NoME-adjusted Stellarium Reckoning

This synchronization scheme is similar to James Strom’s reckoning, but rather than using Stellarium to find a year around 6000 years ago that fits the astronomy described in The Lord of the Rings, I used that open-source astronomy program to find a fitting year around 9000 years ago, due to a note recently published in The Nature of Middle-earth where Tolkien speculates that Iys 310 could have occurred 16000 years ago.

The James Strom reckoning above is a very close match to the moon phases used in the story, which matches the full moon of the night of III 3019 Afteryule 8, and also has Mars low (about 20 degrees above the horizon) in the southern skies of III 3018 Blotmath, and of course a prominent Venus in the evening sky of III 3019 Solmath 15. According to Stellarium, however, the full moon that should fall on the night of Rethe 7/8 actually occurs around dawn on the morning of Rethe 7 by that scheme (which some might consider close enough). Also, the moon on the eve of the destruction of the One Ring should be “four nights old”, so a new moon should occur sometime between dawn on Rethe 21 and dawn on Rethe 22, but in that scheme the new moon occurs on the evening of Rethe 22, making the moon of Rethe 24 three nights old instead.

So I used Stellarium to find a year around 7300 B.C.E. that attempts to meet all of these requirements.

In this scheme, the destruction of the One Ring occurs on a proleptic Gregorian March 16 in 7194 B.C.E. (or Julian May 11), and also happens to align Mid-year’s Day in III 3019 (the day of Aragorn and Arwen’s wedding) with the summer solstice!

Unfortunately this scheme is not perfect either, and the few instances of constellations described in the story are not in the same parts of the sky during the same time of year at this point in the past, which I believe is due to the Earth’s axial precession.

For example, the night the hobbits first encounter a Black Rider shortly after setting out from Hobbiton, the constellation Menelvagor (“the Swordsman of the Sky”, a.k.a. Orion) began to rise late in the night. This constellation usually rises around midnight (or maybe later) on September evenings in modern times, and at those northern latitudes, but only some of the top-most stars of this constellation would have been visible 9000 years ago. From what I can tell in Stellarium, it seems Orion’s belt never makes it above the horizon at this latitude, at any time of the year, around 9000 years ago!

Additionally, it seems these astronomy simulations can not be counted on for a high degree of precision for dates so far back into the past. The description of the F. Espenak and J. Meeus algorithm used by default in Stellarium note that the valid range of usage is “between years -1999 and 3000”. There are other algorithms available in Stellarium’s simulation settings, but only a couple are described as valid as far back as -4000. I used the default Espenak & Meeus algorithm, assuming that it’s close enough for this speculative exercise, and so that anyone else that wishes to see this for themselves will not have to adjust any settings in Stellarium first.

Dates of Interest

As mentioned in the “How to Use these Calendar Simulations” notes above, the events of Middle-earth in the Dates of Interest list are tied to this simulation’s Shire Reckoning calendar, including the events given for the First Age (so the selected First Age event may change if the S.R. year changes when adjusting the Gregorian Date). These dates are listed in descending order, from latest to earliest.

The years in this list correspond to the appropriate Shire-reckoning year or Age of Middle-earth, where S.R. = Shire-reckoning, III = Third Age, II = Second Age, and Iys = First Age Years of the Sun.

Most of the dates in this list come from The Lord of the Rings Appendix B (which lists even more events with years and dates from the Second Age through the Fourth Age), or from some of the other Appendices (such as some of the birth dates), with a few corrections from The Lord of the Rings: A Reader’s Companion. The seasons for First Age events in this list were derived from the text of The Silmarillion, but most of these First Age years were compiled from sites like the First Age Timeline article on Tolkien Gateway, the Henneth Annun Story Archive, and the LOTR Project Timeline. Ultimately these First Age years come from “The Grey Annals” in The War of the Jewels.

There were many more events that occurred in the First Age before the first rising of the Sun and Moon, but I don’t think it makes sense to view those events in the context of these calendars, since the calendars of Middle-earth described by Tolkien in Appendix D are certainly solar calendars.


Shire-reform was enacted sometime between S.R. 1083 - 1122, during the time of Isengrim II. Once enacted, every year of the Shire Calendar always started on the first day of the week and always ended on the last day of the week, by not assigning a day of the week to Mid-year’s Day or the Overlithe days. For these simulations, I am assuming that before Shire-reform was enacted, the current day of the week in the Shire Calendar was the same as the corresponding day of the week that was current in Gondor (since the Shire Calendar was based on the Kings’ Reckoning calendar). Shire-reform was probably enacted in a year that was already supposed to start on the first day of the week, which in this simulation means one of these Shire-reckoning years during the time of Isengrim II:

So for this simulation, I picked the year in the middle of this list as the first year of Shire-reform. Shire-reform was also adopted “eventually” in Bree, but we are not told when, so this simulation also displays the Bree calendar using Shire-reform starting from this year.

Millennial Leap-years

What I’m calling a “Millennial Leap-year” is a year in which the “millennial additions” to the calendars of Númenor or Gondor occurred, as Tolkien described in Appendix D. The “millennial additions” were an addition of 2 days in every millennium of the Kings’ Reckoning calendar (in II 1000, 2000, 3000 and again in III 1000, 2000). See my project’s notes on The Kings’ Reckoning Rules and the Deficit for more details about these “millennial additions”.

Tolkien never specified how the Shire Calendar stayed in sync with the Stewards’ Reckoning calendar by the end of the Third Age, but if the Shire Calendar originated from the Kings’ Reckoning around or before III 1601, then ended up in sync with the Stewards’ Reckoning calendar by the end of the Third Age, it makes sense to me that the Shire Calendar probably incorporated the Kings’ and Stewards’ millennial adjustments around the same time as Gondor. Although another possibility remains that the Shire Calendar incorporated some or all of the adjustments at once as part of the Shire-reform, during the time of Isengrim II between S.R. 1083 - 1122 (III 2683 - 2722), more than 300 years after the last adjustment was made by Hador the Steward. Compare this to the real-world example of how the Gregorian calendar was first introduced in October 1582, but Britain did not adopt it until 1752. So it could have been a couple of centuries before the Hobbits found a “reasonable” year to incorporate the Gondor adjustments into their calendar. Since Shire-reform was the last change to the Shire Calendar that Tolkien mentions in Appendix D, then this is probably the latest time the millennial adjustments would have been incorporated.

The simulations of this project simply add the millennial adjustments to the Shire Calendar in the same years as the calendars of Gondor, though Tolkien never specified whether or not this occurred.

Tolkien also did not give any more details about what this “adjustment” was exactly, so I had to improvise for these simulations. In the tradition of the Eldar calendar that doubles its middle-days every leap-year, I decided to double the leap-day in a “Millennial Leap-year” of the Shire and Gondor calendars in order to accomplish the “millennial additions” of 2 days.

According to the leap-year rules of these calendars, every 4th year is a leap-year, and if this were the only leap-year rule, then a millennial year would also be a leap-year. Since these leap-year rules also omit the leap-day every century, then this additional rule would make a millennial year a common (non-leap) year. So these calendar simulations accomplish the 2-day “millennial additions” in a “Millennial Leap-year” by not omitting the leap-day in each millennial year, and also by doubling that year’s leap-day.

In each “Millennial Leap-year” of the Shire Calendar, I’ve added an extra Overlithe to the other side of Mid-year’s Day. In each “Millennial Leap-year” of the Gondor calendars, I replace Loëndë with 3 Enderi instead of 2; except in the New Reckoning where I honor Frodo by doubling the Cormarë (meaning the Ring-bearer’s birthday celebrations are extended to a 3rd day).

Note the 3 exceptions to the “Millennial Leap-year” rule as interpreted from Tolkien’s statements in Appendix D:

The fact that when Steward Mardil needed to add 2 extra days they were added to a common year, and when Steward Hador needed to add 1 extra day it was added to a leap-year, suggests that they accomplished their additions by also converting those years into “Millennial Leap-years” (and probably by replacing Loëndë with 3 Enderi), as I have done with these simulations, and as described above.

Notes on Tolkien’s Deficit calculations

For all my interest in Appendix D, I was never really interested in Tolkien’s Deficit calculations, since I did not need to analyze Tolkien’s calculations in order to understand the rules of the calendars as presented in Appendix D, and I only needed those rules in order to create these calendar simulations. My understanding of those rules is also the basis of my argument that Rivendell New Year’s Day fell on a March 25th by the end of the Third Age.

Then I came across the Reddit post “Tolkien has reckoned correct in App. D after all” by Andreas Möhn, a.k.a. CodexRegius (apparently reproduced from a Lalaith’s Middle-earth Science Pages blog post with a similar title). Since I was skeptical of Möhn’s conclusion that additional Stewards’ Reckoning rules that Tolkien “failed to specify” explain the Appendix D calculations, I decided to finally examine Tolkien’s Deficit calculations for myself to see if they supported this idea.

Since I’m confident I have accurately reproduced the rules of the Kings’ and Stewards’ Reckoning in these calendar simulations, it was not difficult to use those calculations to assist my own Deficit calculations, and then compare my results with the results of Tolkien and others.

I’ve come to a different conclusion than Möhn, but thanks to one of the insights posted in his blog, I’ve found a simpler explanation for Tolkien’s Deficit figures presented in Appendix D. I am confident that all the rules of the Kings’ and Stewards’ Reckoning are accounted for in Appendix D, but I now think that Tolkien attempted to use deficit calculations for the Second Age years 5501, 5801, and 6462 when discussing the deficit for the Third Age years 2060, 2360, and 3021. I have posted my results on this project’s “The Kings’ Reckoning Rules and the Deficit” page, along with more details about the Kings’ and Stewards’ Reckoning rules, and details on how to work out the math of the Deficit according to these rules.

Leap-years beyond the Third Age

Tolkien did not give any details on how the New Reckoning handled leap-years in the Fourth Age. That leaves me with the following 2 options for this simulation. The first option may be more realistic, but for the simplicity of not inventing new leap-year rules, and to always keep the New Reckoning in sync with Shire Reckoning, I chose option #2:

  1. Restart leap-year calculations according to the count of Fourth Age years in the New Reckoning. This means either altering the Shire Calendar leap-year rules to omit leap-days in the corresponding centuries of the Fourth Age (which means omitting leap-days in S.R. 1520, 1620, 1720, etc.), or not altering the Shire Calendar leap-year rules and continue omitting its leap-days in S.R. centuries (1500, 1600, 1700, etc.). If the traditional Shire Calendar leap-year rules continued into the Fourth Age, but the New Reckoning restarted its calculations, then its Yestarë, Yavannië 30, and Cormarë would be out of sync with the Shire Calendar for 20 years around every century. Also, the Shire Calendar would have to choose a year to make a Millennial Leap-year that would be different than the New Reckoning’s Millennial Leap-year (since those also fall on a centennial year), making these calendars even more out of sync in the meantime.
  2. Ignore the new count of years for the Fourth Age and continue reckoning leap-years in the New Reckoning and the Shire Calendar as if the count of Third Age years had continued. This allows the New Reckoning Yestarë to always correspond to Shire Rethe 25, and New Reckoning Yavannië 30 (or Cormarë in leap-years) to always correspond to Shire Halimath 22. Since IV 1 corresponds to III 3021, then regular leap-years in the New Reckoning calendar will still occur in years divisible by 4, but leap-days omitted at the end of centuries appear to come 20 years early (IV 80, IV 180, IV 280, etc.), and Millennial Leap-years would also come 20 years early in the New Reckoning, but continue to come 600 years early (or 400 years late) in Shire-reckoning years (e.g. S.R. 2400, 3400, 4400, etc.)