# Reading & Writing Elvish Numbers

There are two ways the Tengwar approach numbers. We'll take a look at both in this blog post as well as the step-by-step process of using Christopher Tolkien's method to read (decode) and write (encode) numbers in the duodecimal (base-12) system theoretically favored by the Elves.**General Background:**

Most cultures in our world use a base-10 system for counting. This is the default because of the ease of counting in base-10 when you have 10 fingers. (There are exceptions, of course, like the Mayans using fingers **and** toes, thus base-20 counting. Computers have simple on-off states, thus a base-2 or binary system.)

J.R.R. Tolkien experimented quite a bit with counting systems for his world. The most comprehensive article I've found on the matter is by Thorsten Renk: "Eldarin Numerals". He goes very in depth on the relation between counting systems and vocabulary and naming of numerals. The strongest statement from *The Lord of the Rings: Appendix D* on the matter is that "the Eldar preferred to reckon in sixes and twelves as far as possible", but this is often at odds with other examples of Tolkien's construction of his number systems.

In the end, it *seems* the Elves utilized a duodecimal (base-12) system for reckoning time and mathematics, but everyday language was largely decimal-based with a couple duodecimal influences.

What does this mean when it comes to reading and writing in Elvish Tengwar? It means there are a couple different systems in place, one of which is particularly adaptable to switching between base-10 and base-12 systems. Let's get into the weeds!**System 1 of 2: Christopher Tolkien**

There are two number systems in Tolkien’s Tengwar. The first system was given to readers from Christopher Tolkien. It was published first, so it’s the more widely known of the two systems. Christopher’s system uses distinct characters not used anywhere else in the Tengwar. Because it’s so easy to distinguish visually from the rest of the Tengwar, this is my preferred method. It is also the adaptable system that can be utilized both for base-10 and base-12.

Twelve distinct Tengwar exist to denote each of the 12 numerals: 0 through 11. In base-10, we would only utilize the Tengwar for 0 through 9. In base-12, all twelve Tengwar would be used. Because our Arabic system of counting only gives us characters for 0 through 9, the notation used for 10 and 11 in base-12 can vary quite a lot by users. For the purposes of this guide, I'll use the Dwiggins style notation of X ("dek") for the equivalent of 10, and then E ("el") for the equivalent of 11. So the Tengwar with their associated Arabic counterparts is as follows.

The other thing that sets this system apart is that the Elves count in ascending magnitude, whereas we IRL count in descending magnitude. So for us, the order of our numbers start high and work smaller: thousands, hundreds, tens, ones. The Elves are the opposite, counting their ones first, then progressing larger to their other multiples. In base-10, this means ones, tens, hundreds, thousands, etc. In base-12, it equates to ones, twelves, 114s, etc.

So a longer number like "207,961" in English (base-10), would be spelled out 1-6-9-7-0-2 in Elvish Tengwar (if we remain in base-10).

We'll revisit this system and its idiosyncrasies between base-10 and base-12 in more detail after we cover the second system.**System 2 of 2: J.R.R. Tolkien**

The second system for writing numbers was given to us by J.R.R. Tolkien himself. However, because this was published much later (2012) and uses pre-existing Tengwar characters to denote each digit, this version is typically less popular. It’s redeeming quality is that these digits are written left-to-right like the rest of the Tengwar, so the numbers are in the same descending magnitude that we're accustomed to using in English. This means our example of "207,961" would be written 2-0-7-9-6-1, just the same as we would expect in English. This second system from J.R.R. Tolkien is also **solely** base-10. There is no flexibility for the Elves' duodecimal counting here.**My Personal Preferences:**

Every person who decides to learn the Elvish Tengwar is free to use either of these two systems for writing out numerals. Both are entirely valid and functional! My personal preference, however, has always been Christopher's system. And when I write out my Elvish Letters for the Elvish Letter Fellowship Club (ELF-Club), I also convert everything into the duodecimal (base-12) system that Tolkien mentions the Elves preferred. This means that decoding my Elvish Letters is a multi-step process when it comes to numbers. Let's take a look at an example date and both encode it into Tengwar, and then decode it back into our Arabic Numeral System we use in English.

The first thing you'll notice in this example is that all the numbers have a dot beneath them. This is the way the Elves distinguished base-12 numbers from base-10. If you see these Tengwar without any dots, you can assume that the number is written in base-10 (the decimal system). Dots like this example, or tiny circles rather than dots, mean the number is written in the duodecimal system! I prefer using duodecimal, even though it ends up being more complicated.

Number-by-number, the example reads "5-4, Ethuil, 8-1".**STEPS FOR DECODING:**

1. Switch Numerals from Ascending to Descending

2. Switch Numerals from Base-12 to Base-10

3. Note Full Date: Day + Season + Year

4. Translate Season from Neo-Sindarin to English

5. Consult Calendar of Imladris to find Gregorian Equivalent Date

Let's go through this process together with visual aides!**Step 1: Switching from Ascending to Descending**

Our two numbers here read "5-4" and "8-1" on the page. This means we have the ones place followed by the twelves place in base-12. Let's flip things so we at least have the larger multiples first and the ones place on the left side.

"5-4" -> "4-5"

"8-1" -> "1-8"

I retain the dashes here just to show that this is still base-12. That leads right into our next step.**Step 2: Switch from Base-12 back to Base-10 (Decimal)**

If you wanted to do this without any digital aid, you could! It'll just bend your brain a bit.

I always use a digital converter to save time. The one linked allows you to simply type in the base-12 number in the "input" section and then tap "convert" to get the output listed in the "Results" section below that.

For the sake of example, though, let's go through this once in long-form! In the decimal system we're used to, each order of magnitude in our written number sequences is a multiple of ten. So we have the ones place, the tens place (1x10=10), the hundreds place (1x10x10=100), and onward. Every decimal spot we move over is another x10.

The same exact thing is true in base-12... except we're multiplying by 12 each time. So we begin with the ones place, and then the twelves (1x12=12), and then the 144s (1x12x12=144).

In our letter's example, "4-5" means there's a 4 in the twelves place and a 5 in the ones place. So 4x12 = 48, and then 5x1=5. If we add those two together, we get our equivalent in base-10. 48+5=53.

So "4-5" in base-12 = "53" in base-10.

Our second number is even easier! "1-8" means there's a 1 in the twelves place and 8 in the ones place. So 1x12=12, and 8x1=8. Then we add: 12+8=20.

So "1-8" in base-12 = "20" in base-10.**Step 3: Note Full Date in Order**

If we add all the above elements together, this gives us the final reading of *"53 Ethuil 20"* or the 53rd day of the Ethuil season, Year 20.

(Extra Note: Since there's no notation on which Age we're dealing with, one can assume it's the First Age. Anyone writing in that time period wouldn't **know** they were in the "First Age" until much later when that Age ended and a second one began.)**Step 4: Translate Season from Neo-Sindarin to English**

The Calendar of Imladris starts at a different time of the year compared to our Gregorian Calendar. The Elvish calendar begins around the end of March each year. This is to have the Elvish calendar correspond with the seasons of the yearly growth cycle.

There are six months/seasons in the Calendar of Imladris. I'll list them below with their Neo-Sindarin, Quenya, and English names.

🌼 Ethuil -- Tuilë -- Spring

☀️ Laer -- Lairë -- Summer

🍇 Iavas -- Yávië -- Autumn/Harvest

🍂 Firith -- Quellë -- Fading

❄️ Rhîw -- Rhívë -- Winter

🌱 Echuir -- Coirë -- Stirring

So our example in the letter is "Ethuil" -> "Spring"**Step 5: Consult Calendar of Imladris to find Gregorian Equivalent Date**

Because of how the Elves handled Leap-Years in their calendar (once every 12 years), the exact dates of the Calendar of Imladris aren't always fixed perfectly to the dates in the Gregorian Calendar (whose Leap Years are every 4 years instead).

So when consulting a Calendar Simulator, just keep in mind that we're not trying to be super exact here when converting dates from my Elvish Letters. This is just to give you a general idea of what time of year in our calendar each letter was written. This step is entirely optional!

For our example: 53rd Day of Ethuil/Spring, you'll want to scroll down to the "Rivendell Reckoning". Don't worry about the "Synchronization Settings". In the Rivendell Reckoning section, I suggest switching the "Month View" to "Horizontal" to make the chart resemble our Gregorian Calendar. You can change the Language to "Sindarin" or "English" if you prefer them!

To find your equivalent day, just tap "This Year" so that the calendar shows the entire calendar year in one long vertical chart. Spring is the first season of the year, so look for the 53rd Day.

If you don't mess with any synchronization settings, you should see that the 53rd Day of Spring = May 18th, 2024. So we generally know that in this specific example, Daeron wrote a letter to Maglor in mid-May of the 20th year of the First Age.

From here, you can take a looksie at Middle-Earth Timelines to investigate what other events might have happened around that time. In this case, clicking to the First Age and scrolling down to the Years of the Sun, you'll see that FA 20 marked the Feast of Mereth Aderthad. You can then investigate more about this event in the timeline if you like. Go as deep as you like down the rabbit hole of Tolkien Gateway!**Encoding A Date from English into Elvish Tengwar**

You now know how to DECODE a Date given in one of my Elvish Letters! Huzzah! But what if you want to ENCODE one for yourself? Let's take a look at doing this in REVERSE order.**STEPS FOR ENCODING:**

1. Consult Calendar Simulator for Equivalent Elvish Date

2. Translate Season from English to Neo-Sindarin

3. Note Full Date: Day + Season + Year

4. Switch Numerals from Base-10 to Base-12

5. Switch Numerals from Descending to Ascending

Let's choose a sample date! We know that Frodo's birthday in *The Lord of the Rings* is September 22nd. Say you wanted to send out invitations to celebrate Hobbit Day with your friends next year (2025). We can convert September 22nd, 2025 into Elvish!**Step 1: Finding the Elvish Equivalent Day**

Using our Calendar Simulator, you'll want to scroll to the "Gregorian Date" section right before the Shire Reckoning and Rivendell Reckoning tables. Here, you can input the date September 22nd, 2025. This will make the equivalent date highlight in yellow on all the calendars. Scrolling down to the Rivendell Reckoning, you'll see the highlighted block is the 54th day of Autumn/Harvest (🍇*Iavas* in Neo-Sindarin). This is the last day of the season before the multi-day *Enedhor* "Middle-day" Festival each year.

Sept 22nd, 2025 -> 54 Iavas 2025**Step 2: Translate Season from English to Neo-Sindarin**

Optional step, of course, but fun if you want to give the date in Elvish Tengwar. The Simulator used in Step 1 will have the equivalent for each season/month in the Calendar of Imladris, so simply take note of it like I did above!**Step 3: Note Full Date**

I also easily work this into Step 1. Just orient your date as Day + Season + Year to keep things standard. I know us Americans tend to use the "Month + Day, Year" format, but ascending from day to month to year makes a lot of sense for writing dates in Elvish, since the ascending order is how they write their numerals as well!**Step 4: Switch Numerals from Base-10 to Base-12**

Again, using our Digital Converter, you'll want to scroll down and alter the settings. We're going FROM base-10 TO base-12, so if it's set up the opposite, you can tap the button that switches the settings. Plug in "54" as your Input, and then tap Convert. Below, you'll see the result is listed as "46 base-12". So, for notation purposes here:

"54" in base-10 = "4-6" in base-12

Then our longer year number! Input "2025" with those settings, and you should get "1209 base-12" as your result.

"2025" in base-10 = "1-2-0-9" in base-12**Step 5: Switch Numerals from Descending to Ascending**

Our last step before we can write it out! Let's flip the numerals to be in ascending order!

"4-6" -> "6-4"

"1-2-0-9" -> "9-0-2-1"

So what we'll be actually writing out in Tengwar is: *"64 Iavas 9021"*.**Final Step: Writing in Tengwar**

Consulting the tables from the beginning of this post, write out each number. Since we're using base-12, don't forget to put a dot below every digit! A single dot between the Day, Season, and Year will act like commas. If you're unfamiliar with the rest of the Tengwar Alphabet, you can use Tecendil to see how your season name is spelled. (In the Settings, you'll want to ensure the "Mode" is set to match the language you're using. I default to "Sindarin (General Mode)" for most of my letters, since I translate my season/month names into Neo-Sindarin before writing them out.)

This is how our date should look, all written out in Tengwar!

It's quite the adventure to learn Tengwar. While numbers and dates can be on the more complex side, I hope you find this guide helpful and that you use its linked resources to help you if you ever craft your own Tengwar dates or invitations!