Lesson 23
Sumerian Numbers
A Comprehensive Guide to Sumerian Numerals
In this lesson, you’ll learn all about Sumerian numbers! We’ll be delving into their development first, then I’ll provide you with a quick reference list before doing a detailed breakdown of each Sumerian numeral.
We’ll be focusing on Sumerian cardinal numbers for the time being, as creating ordinal numbers requires a better grasp the genitive case, which we’ll be delving into in an upcoming lesson.
NOTE: This ‘lesson’ is information-intensive, and thus better used as a reference guide, so you may want to bookmark it for future use!
Jump to Section
Vocabulary to Memorize
I highly recommend memorizing these Sumerian words, as you’ll encounter them often in the upcoming lessons!
- a-rá 𒀀𒁺 prep., mathematical function ‘times’ (OS x8, OA x196, NS x6489, OB x572).
- lá (lal) 𒇲 v., to be small, less, low value, insignificant; to make small, reduce, diminish, subtract; mathematical function ‘minus’ (OS x2,666, OA x1974, NS x12,064, OB x112).
- sìla 𒋡 n., unit of volume equivalent to approximately 1 liter.
- šár 𒊹 n., totality; world; horizon; ball. num., three thousand six hundred (3,600).
- še n., barley, grain; length of measurement equivalent to approximately 1.7 centimeters; surface measurement of approximately 432 square barley corns; unit of volume equivalent to approximately 1.7 liters; 1/180th of silver shekel (approx. 0.05 grams).
Vocabulary--Full List
The majority of this lesson is a list of numbers written out in their various forms over the centuries. For this reason, I’ve limited the vocabulary section to all non-numbers. Everything will be listed in the Sumerian-to-English Dictionary.
- a-ra 𒀀𒊏 prep., mathematical function ‘times’ (OB x6).
- a-rá 𒀀𒁺 prep., mathematical function ‘times’ (OS x8, OA x196, NS x6489, OB x572).
- a-rá-a-rá 𒊏 prep., mathematical function ‘times’ (OB x1).
- ba-an 𒁀𒀭 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (OS x69, OA x8, NS x17, OB x6).
- ĝešba-an 𒄑𒁀𒀭 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (NS x18, OB x31).
- giba-an 𒄀𒁀𒀭 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (NS urudba-an 𒍏𒁀𒀭 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (NS x2).
- ba-anzabar 𒁀𒀭𒌓𒅗𒁇 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (NS x1).
- bàn 𒌉 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (OS x1).
- bán 𒑏 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (NS x2, OB x21).
- x12, OB x1).
- dug bàn 𒂁𒑏 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (OB x2).
- ĝeš bàn 𒄑𒑏 n., unit of capacity equivalent to 10 to 6 sìla 𒋡 depending on the period (OA x1, NS x1, OB x5).
- bur 𒁓 n., square surface measurement of approximately 6.5 hectares (OA x11).
- bùr 𒌋 n., square surface measurement of approximately 6.5 hectares (OA x2, NS x146, OB x6).
- bùriku 𒌋𒃷 n., square surface measurement of approximately 6.5 hectares (OB x3).
- bùr–bùr–bùr iku𒌋𒌋𒌋𒃷 n., square surface measurement of approximately 6.5 hectares (OBx1).
- gur 𒄥 n., unit of capacity equivalent to 144 sìla 𒋡 in OS, or 300 sìla 𒋡 in OA/NS (OS x1726, OA x2927, NS x49312, OB x804).
- igi N ĝál 𒅆N𒅅 nu., fraction indicating one-Nth (lit., ‘it is the reciprocal of the number’) (OA x56, NS x1788, OB x39).
- iri 𒌷 prep., mathematical function ‘times’ (OB x1).
- iriki 𒌷𒆠 prep., mathematical function ‘times’ (OB x1).
- lá (lal) 𒇲 v., to be small, less, low value, insignificant; to make small, reduce, diminish, subtract; mathematical function ‘minus’ (OS x2,666, OA x1974, NS x12,064, OB x112).
- sìla 𒋡 n., unit of volume equivalent to approximately 1 liter.
- šár 𒊹 n., totality; world; horizon; ball. num., three thousand six hundred (3,600).
- še n., barley, grain; length of measurement equivalent to approximately 1.7 centimeters; surface measurement of approximately 432 square barley corns; unit of volume equivalent to approximately 1.7 liters; 1/180th of silver shekel (approx. 0.05 grams).
- duggur 𒂁𒄥 n., unit of capacity equivalent 300 sìla 𒋡 in OA/NS (OB x1).
The Sumerian Numerical System
The Sumerian numerical system was sexadenery and proceeded as:
- 1-10
- 10-60
- 60-600
- 600-3,600
- 3,600-36,000
- 36,000-216,000
This ingenious system, which some have speculated was long in use before the development of writing, is a hybrid of a base-60, and a base-10 system. Not only does it allow for counting on five-fingered hands, it also allows for divisions of 3 and 6 without leaving a remainder.
FUN FACT: The Babylonians used this earlier Sumerian system to develop the 360-degree circle, and divide the day into 24 hours of 60 minutes made up of at seconds each.
Pronouncing Sumerian Numbers
The oldest Sumerian number pronunciation guide comes from tablet TM 75.G. 2198, which has been dated to around 2500 BCE. While it provides phonetic guidance for numbers 1 – 10, there is still debate as to the precise pronunciation.
I’ve done my best to provide insight into how these might have sounded or been read, but you’re welcome to use the standard pronunciations.
Reading Sumerian Numerals
In the most distant times, Sumerian numerals were written with archaic symbols that aren’t available in standard Unicode forms, and thus difficult to write here (see image below). As time went on, these symbols were replaced with cuneiform values.
NOTE: The only archaic values I was able to find in Unicode were 𒑝 and 𒑞, which seems helpful to precisely no one.
Unfortunately, numerical values in transliteration often appear as standard English numerals, as in ‘1 sìla 𒋡’ (approx. 1 litre), ‘600 še’ (barley), etc. They also appear as combinations of numbers, word-signs, and other values, as in 3(šár)@v 𒐥 (10,800).
While we know the cuneiform signs for many of these, we don’t always know how they were read. For example, 3(šár)@v 𒐥 may have been read ‘šar-eš(u)’, ‘šar-(a)-rá-eš(u)’, or some other way entirely.
This means that when reading a number in an untranslated or transliterated text, you’ll have to use the date, period, and location of your text and take your best guess as to how it would have been read. When in doubt use the oldest or most common forms, which I’ve provide in the sections below.
When dealing with compound numbers, like 3(šár)@v 𒐥, it’s probably safe to put the largest multiplier first: šár-eš (3600×3).
Finally, despite being written with the numerical value before the item, as in ‘1 sìla 𒋡’, the noun is likely meant to be read before the number. So instead of saying áš sìla 𒀸𒋡, you’d say sila áš 𒋡𒀸.
Sumerian Arithmetic
Unfortunately, Sumerian lacks symbols for basic mathematical operations, which means imin ía 𒅓𒐊 could mean 7×5 or 7+5.
It’s possible that syllable or word emphasis played a role in determining these functions. Or perhaps other words or phonetic elements were used which the speaker or reader would have understood.
In some cases, we have clear examples of the words ‘minus’ and ‘times’ being written to indicate these functions.
Minus (-)—LÁ (LAL) 𒇲
There are examples of lá 𒇲 (minus/less) being used to indicate a numeral, as in niš lá eš 𒎙𒇲𒌍 (17) (lit., 20-3), so we can assume other Sumerian numbers were created in this way. But most often, lá 𒇲 was used in mathematical calculations.
Times (x)—A-RÁ 𒀀𒁺
The word a-rá 𒀀𒁺 was used to indicate ‘times’, as in 7(diš) a-rá 7(diš) 𒐌𒀀𒁺𒐌 (7×7).
Variations of a-rá 𒀀𒁺
The Fraction 1/Nth
To express the fraction 1/Nth, (the ‘N’ in dicates ‘number’) the phrase igi N ĝál was used, as in igi 6(diš) ĝál 𒅆𒐋𒅅 one-sixth (1/6).
Sumerian Numbers—Quick Reference
While we’ll be breaking each of these Sumerian numerals down shortly, the oldest and/or the most common cardinal Sumerian numbers and their most likely pronunciations are as follows.
NOTE: I’ve put my preferred choice of pronunciation of numbers 1 – 10 at the beginning. These reflect both the oldest pronunciations known to us, and happen to be the versions which employ assonance and rhyme; a common trait in the counting schemes of some other languages.
NOTE: When counting items aloud, diš 𒁹 is thought to be preferred to aš 𒀸.
CHALLENGE: Practice counting 1-10 in Sumerian every day, the same way you would have learned to count in your native language as a child.
- 1—aš 𒀸 (ašu—aš, iš(u))
- 2—min 𒈫 (minu—min(u))
- 3—eš 𒌍 (ešu—eš, ešam, išam, eš(u)am)
- 4—límmu 𒇹 (limu—limmu)
- 5—ía 𒐊 (ya—i, a, ya)
- 6—àš 𒐋 (yašu—(i)aš(u), yaš, a-aš(u))
- 7—imin 𒅓 (yaminu—imin(i), umin(u), yamin)
- 8—ussu 𒐍 (ussu—us(u)am, i/a-wes(u))
- 9—ilimmu 𒑆 (yalimu—ilimmu)
- 10—u 𒌋 (huwamu—u, yu, hawimu, uwamu)
- 20—niš 𒎙
- 30—úšu 𒌍
- 40—nimin 𒐏
- 50—ninnu 𒐐
- 60—ĝéš 𒐕
- 600—ĝéš-u 𒐞
- 3,600—šár 𒊹
- 36,000—šaru (šár’u) 𒐬
Sumerian Numbers—Detailed Breakdown
Sumerian Numbers 1-10
1—AŠ 𒀸, DIŠ 𒁹, DILI 𒀸
Generally speaking, the Sumerian numeral one (1) is written aš 𒀸, diš 𒁹, or dili 𒀸 depending on the context. However, when counting aloud, it was likely spoken as diš 𒁹.
Variations of AŠ 𒀸
Variations of DIŠ 𒁹
- diš 𒁹 adj., single, unique. num., one (1) (OS x4, OA x5, NS x21, OB x113).
- di-ta 𒁲𒋫 adj., single, unique. num., one (1) (OB x7).
- te-ša 𒋼𒊭 adj., single, unique. num., one (1) (OB x4).
- dišₓ(U) 𒌋 adj., single, unique. num., one (1) (OB x2).
- gud-e-ša 𒄞𒂊𒊭 adj., single, unique. num., one (1) (OB x1).
- kud-e-ša 𒋻𒂊𒊭 adj., single, unique. num., one (1) (OB x1).
- te-e-ša 𒋼𒂊𒊭 adj., single, unique. num., one (1) (OB x1).
Variations of DILI 𒀸
2—MIN 𒈫
The most common writing of the Sumerian numeral 2(dišt) (the numeral two (2)) is not currently available in Unicode. However, 2(dišt) was likely pronounced mí-n(u) 𒊩𒉡.
3—EŠ5 𒐈
In the oldest pronunciation guide we have, the Sumerian number three (3) was said to be pronounced iš11-ša-am, which is essentially the sounds /i/ or /e/ + /š/ + the copula /m/.
NOTE: While a few numbers were written as being pronounced with a copula, some—myself included—have speculated that this was a carry-over from earlier periods, wherein the numeral would have acted differently depending on it’s use in the sentence. Thus the pronunciation guide might not necessarily reflect its standard pronunciation.
- eš 𒌍 num., three (3) (OS x4, NS x45, OB x15).
- eš5 𒐈 num., three (3) (OS x2, OA x1, NS x3, OB x71).
- 3(diš) 𒐈 num., three (3) (NS x3, OB x12).
- eš-a-bi 𒌍𒀀𒁉 num., three (3) (NS x9).
- peš 𒄫 num., three (3) (OB x5).
- eš6 𒐁 num., three (3) (OB x2).
- 3(dišt) X num., three (3) (OA x1).
- eš₃ 𒀊 num., three (3) (OB x1).
- àm-mu-uš 𒀀𒀭𒈬𒍑 num., three (3) (OB x1).
- àm-muš 𒀀𒀭𒈲 num., three (3) (OB x1).
- mi-úš 𒈪𒌀 num., three (3) (OB x1).
4—LÍMMU 𒇹
The Sumerian number four (4) was pronounced as li-mu, lim-mu, or lim-u.
6—ÀŠ 𒐋
The oldest pronunciation of the Sumerian numeral six (6) is a-šu 𒀀𒋗, resulting in àš 𒐋.
The pronunciation of /yaš/ has also been suggested, as it would reflect a contraction of ía 𒐊 + aš 𒐋 (5+1). Additionally, the /a/ of àš 𒐋 has been suggested as /a/, /ay/, /aw/, and /ya/.
7—IMIN 𒅓
The Sumerian numeral seven (7) imin 𒅓 was said to be pronounced ú-mi-nu 𒌑𒈪𒉡 in the oldest guide we have.
It has been suggested that the imin 𒅓 is a combination of ía 𒐊 and min(u) 𒈫 (5+2). If so, ya-min(u) seems a likely pronunciation.
8—USSU 𒐍
In the earliest records, the Sumerian numeral eight (8) was said to be pronounced ú-sa-a(m); in other words /us/ + /am/.
It’s worth noting that when counting on two hands, the number 8 represents the third digit, and both 8 and 3 are listed in the pronunciation guide with the copula àm 𒀀𒀭. However, this seems to be the only connection between the two.
- ussu 𒐍 num., eight (8) (OB x8).
9—ILIMMU 𒑆
It has been suggested that the number 9 is a combination of ía 𒐊 and límmu 𒇹 (5+4). While ì-li-mu is the oldest known pronunciation, ya-li-mu may be more appropriate.
- ilimmu 𒑆 num., nine (9) (OB x5).
Sumerian Numbers 20 - 60
20—NIŠ 𒎙
The Sumerian number twenty (20) is its own word, or so it’s thought.
- niš 𒎙 num., twenty (20) (OB x19).
30—ÚŠU 𒌍
The Sumerian number thirty (30) is likely a combination of eš 𒌍 and u 𒌋 (3×10).
- úšu 𒌍 num., thirty (30) (OB x15).
40—NIMIN 𒐏
The Sumerian word for forty (40) is a clear combination of niš 𒎙 and min 𒈫 (20×2).
- nimin 𒐏 num., forty (40) (OB x9).
60—ĜÉŠ(D) 𒐕
The original reading/pronunciation of ĝéš was likely ĝešd, as early spellings involving the genitive case marker result in such spellings as 60-da 𒐕𒁕 (of sixty). The origins of the word are still up for debate.
Sumerian Numbers 600 – 216,000
600—ĜÉŠ-U 𒐞
The Sumerian numeral six hundred (600) is literally ĝéš 𒐕 times u 𒌋 (60×10).
- ĝéš-u 𒐞 num., six hundred (600) (Post-OB x10).
3,600—ŠÁR 𒊹
The Sumerian number three thousand six hundred (3,600) is its own word, which is depicted by a solid sphere. The word šár 𒊹 also means all, totality, horizon, and world, as well as innumerable, making 3,600 something of a special number to the Sumerians, as it represented completion.
FUN FACT: The importance placed on the number 3,600 is the reason Zecharia Sitchin believed the 12th planet returned every 3,600 years with the Anunnaki, whom he asserted were a race of extraterrestrials which genetically manipulated human beings.
- šár 𒊹 num., three thousand six hundred (3,600) (OS x16, NS x10, OB x267).
- šár-šár 𒊹𒊹 num., three thousand six hundred (3,600) (OS x1, NS x4, OB x36).
- ša 𒊭 num., three thousand six hundred (3,600) (OB x3).
- ša-ar-ša-re 𒊭𒅈𒊭𒊑 num., three thousand six hundred (3,600) (OB x2).
- ša-re 𒊭𒊑 num., three thousand six hundred (3,600) (OB x1).
216,000—ŠÁR-GAL 𒊹𒃲
The Sumerian number two hundred sixteen thousand (216,000) literally translates as ‘big 3,600’ (216,000 ÷ 60). It is also written šárĝeš(d) 𒊹𒁹, but since I couldn’t find specific attestations, I didn’t include it below.
Additional Sumerian Numerals
While no pronunciation guide for numbers 11-19 exists, it’s probably safe to assume they were created by combining 10 and the single digit in question, as in u-àš, u-min, u-eš etc.
However, we do have examples of the following Sumerian numerals being read as:
- 17—niš lá eš (20-3)
- 18—niš lá ussu (20-2)
- 19—niš lá aš (20-1)
- 47—ninnu lá eš (50-3)
- 120—ĝeš-min (60×2)
- 240—ĝeš-limmu (60×4)
- 420—ĝeš-umin (60×7)
- 1200—ĝeš-u-min (600×2)
- 72,000—šár-niš (3600×20)
- 180,000—šár-ninnu (3600×50)
- 12,960,000—šár-gal-šu-nu-tag-ga (lit., big 3600 untouched)
Cuneiform Numbers in Transliteration
When reading transliterated Sumerian documents, you’ll often see either a simple numeral, or a combination of a number, sign, and additional characters. I’ve compiled a reference guide containing those which are accompanied by a standard cuneiform symbol for easy reference.
While you don’t need to memorize any of these, it might be a good idea to familiarize yoursel with them, and bookmark this page for future reference!
With the exception of the single-digit variations of aš 𒀸, the most likely reading/pronunciation of compound numerals, such as 2(šár) 𒐣 (7,200) were likely read with the base number followed by the multiplier, as in šár-min, šár-eš(u), šár-lim(m)u, etc.
Multiples of 1—AŠ 𒀸
The following are all variations of the aš 𒀸. As you can see, they all point either to the right, or are angled toward the bottom right. They are likely read/pronounced identically to their single-digit counterparts: min(u), eš(u/am), lim(m)u, etc.
- 2(aš) 𒐀 num., two (2).
- 2(aš@t) 𒑊 num., two (2).
- 3(aš) 𒐁 num., three (3).
- 3(AŠ~b) 𒐻 num., three (3).
- 3(aš@t) 𒑋 num., three (3).
- 4(aš) 𒐂 num., four (4).
- 4(AŠ~a) 𒐽 num., four (4).
- 4(aš@t) 𒑌 num., four (4).
- 5(aš) 𒐃 num., five (5).
- 5(aš@t) 𒑍 num., six (6).
- 6(aš) 𒐄 num., six (6).
- 6(AŠ~a) 𒑀 num., six (6).
- 6(aš@t) 𒑎 num., six (6).
- 7(aš) 𒐅 num., seven (7).
- 7(AŠ~a) 𒑁 num., seven (7).
- 8(aš) 𒐆 num., eight (8).
- 9(aš) 𒐇 num., nine (9).
Multiples of 1— DIŠ 𒁹
While diš 𒁹 was used when counting the number one, the following variations of diš 𒁹 are likely read/pronounced identically to their single-digit counterparts: min(u), eš(u/am), lim(m)u, etc.
- 1/3(diš)~e 𒑥 num., 1/3.
- 2/3(diš)~e 𒑦 num., 2/3.
- 3(diš) 𒐈 num., three (3).
- 4(diš) 𒐉 num., four (4).
- 5(diš) 𒐊 num., five (5).
- 6(diš) 𒐋 num., six (6).
- 7(diš) 𒐌 num., seven (7).
- 7(diš)~a 𒑂 num., seven (7).
- 7(diš)~b 𒑃 num., seven (7).
- 8(diš) 𒐍num., eight (8).
- 9(diš) 𒐎 num., nine (9).
- 9(diš ~a) 𒑇 num., nine (9).
- 9(diš ~b) 𒑈 num., nine (9).
- 9(diš ~c) 𒑉 num., nine (9).
Multiples of 10—U 𒌋
- 4(U) 𒐏 num., forty (40).
- 4(U)~v 𒑩 num., forty (40).
- 4(U)@v 𒑧 num., forty (40).
- 5(U) 𒐐 num., fifty (50).
- 5(U)~v 𒑪 num., fifty (50).
- 5(U)@v 𒑨 num., fifty (50).
- 6(U) 𒐑 num., sixty (60).
- 6(U)~v 𒑫 num., sixty (60).
- 7(U) 𒐒 num., seventy (70).
- 7(U)~v 𒑬 num., seventy (70).
- 8(U) 𒐓 num., eighty (80).
- 8(U)~v 𒑭 num., eighty (80).
- 9(U) 𒐔 num., ninety (90).
- 9(U)~v 𒑮 num., ninety (90).
Multiples of 60—ĜÉŠ(D) 𒐕
- 1(ĝéš) 𒐕 num., sixty (60).
- 2(ĝéš) 𒐖 num., one hundred twenty (120).
- 3(ĝéš) 𒐗 num., one hundred eighty (180).
- 4(ĝéš) 𒐘 num., two hundred forty (240).
- 5(ĝéš) 𒐙 num., three hundred (300).
- 6(ĝéš) 𒐚 num., three hundred sixty (360).
- 7(ĝéš) 𒐛 num., four hundred twenty (420).
- 8(ĝéš) 𒐜 num., four hundred eighty (480).
- 9(ĝéš) 𒐝 num., five hundred forty (540).
Multiples of 600— ĜÉŠ-U 𒐞
- 1(ĝešu) 𒐞 num., sixty hundred (600).
- 2(ĝešu) 𒐟 num., one thousand two hundred (1,200).
- 3(ĝešu) 𒐠 num., one thousand eight hundred (1,800).
- 4(ĝešu) 𒐡 num., two thousand four hundred (2,400).
- 5(ĝešu) 𒐢 num., three thousand (3,000).
Multiples of 3,600—ŠÁR 𒊹
- 2(šár) 𒐣 num., seven thousand two hundred (7,200).
- 3(šár) 𒐤 num., ten thousand eight hundred (10,800).
- 3(šár)@v 𒐥 num., ten thousand eight hundred (10,800).
- 4(šár) 𒐦 num., fourteen thousand four hundred (14,400).
- 5(šár) 𒐧 num., eighteen thousand (18,000).
- 6(šár) 𒐨 num., twenty-one thousand six hundred (21,600).
- 7(šár) 𒐩 num., twenty-five thousand two hundred (25,200).
- 8(šár) 𒐪 num., twenty-eight thousand eight hundred (28,800).
- 9(šár) 𒐫 num., thirty-two thousand four hundred (32,400).
Multiples of 36,000—ŠARU (ŠÁR’U) 𒐬
- 1(šaru) 𒐬 num., thirty-six thousands (36,000).
- 2(šaru) 𒐭 num., seventy-two thousand (72,000).
- 3(šaru) 𒐮 num., one hundred eight thousand (108,000).
- 3(šaru@v) 𒐯 num., one hundred eight thousand (108,000).
- 4(šaru) 𒐯 num., one hundred forty-four thousand (144,000).
- 5(šaru) 𒐰 num., one hundred eighty thousand (180,000).
- 6(šaru) 𒐱 num., two hundred sixteen thousand (216,000).
Units of Measurement
The following units of measurement come with their own signs.
Multiples of BÁN (6-10 litres)
- 1(bán) 𒑏
- 2(bán) 𒑐
- 3(bán) 𒑑
- 4(bán) 𒑒
- 5(bán)/4(bán@v) 𒑓
- 5(bán@v)𒑕
- 6(bán) 𒑔
- 1(diš).1(bán) 𒁹𒑏
- 1(diš).2(bán) 𒁹𒑐
- 1(diš).3(bán ₂) 𒁹𒑑
Multiples of BÙR (6.5 Hectares)
- 1(buru) 𒐴
- 2(buru) 𒐵
- 3(buru) 𒐶
- 4(buru) 𒐸
- 5(buru) 𒐹
Fractions of GUR 𒄥 (144-300 Litres)
- ½(gur) 𒑤
- ¼(gur) 𒑣
Your Sumerian Language Journey Continues!
In the next lesson, you’ll learn all about the conjugational prefix /i/, as we begin our deep dive into the Sumerian verbal chain and all its elements, so be sure to subscribe to my substack to get all of my articles as soon as they post!
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Conjugationаl Prefix /I/
