Ancient Number Systems

This collection gathers every number system that Unicode encodes as its own set of signs, apart from the Roman numerals, which have their own page (Roman Numeral Symbols). Ten systems are here: Attic Greek numerals with the local signs of other Greek cities and the money, measure and fraction signs of Greek papyri; the alphabetic Greek numerals' extra letters Ϛ Ϟ Ϡ and the keraia; Chinese counting rods and tally marks; Mayan numerals; Kaktovik numerals; Indic Siyaq and Ottoman Siyaq accounting numbers; Rumi numerals from Fez; Coptic Epact numbers; Sinhala archaic numbers; and the North Indic fraction and rupee marks. Every chart runs from the smallest value to the largest, the way the system's own users wrote it, so you can read a number straight off the grid.

They fall into three families. Additive systems (Attic Greek, Sinhala) have a sign for 1, 5, 10, 50 and so on and repeat them: ΔΔΔ is 30. Ciphered systems (alphabetic Greek, Rumi, Coptic Epact, both Siyaq sets) have a separate sign for every unit, every ten and every hundred, so a three-figure number is exactly three signs and needs no zero. Place-value systems (counting rods, Mayan, Kaktovik) have digits whose value depends on their position, exactly like 2026, and those are the ones that have or need a zero: 〇, the Mayan shell 𝋠 and the Kaktovik 𝋀. The ordinary digit styles are in Number Symbols, modern fractions in Fraction Symbols, and the Greek alphabet itself in Greek Letters.

All of these live in the Supplementary Multilingual Plane, which is why most phones show them as boxes; the section on fonts below says which Noto font draws each set. They were added over many years: counting rods in Unicode 5.0 (2006), Rumi and the North Indic forms in 5.2 (2009), Attic numerals in 4.1 (2005) with Byzantine additions in 7.0 and 9.0, Coptic Epact and Sinhala archaic numbers in 7.0 (2014), Mayan numerals, Indic Siyaq and the tally marks in 11.0 (2018), Ottoman Siyaq in 12.0 (2019) and Kaktovik numerals in 15.0 (2022).

Ancient Greek numbers: Attic numerals, alphabetic numerals and the papyri signs

The oldest Greek system is the Attic or acrophonic one, used on Athenian inscriptions from about the 7th century BC until the 1st century BC: tribute lists, temple inventories and the building accounts of the Parthenon. Acrophonic means the signs are the first letters of the number words: Ι is one stroke, 𐅃 (an old form of Π) is pente 5, Δ is deka 10, Η is hekaton 100, Χ is khilioi 1,000 and Μ is myrioi 10,000. Fifty, 500, 5,000 and 50,000 are a five with the smaller sign tucked inside it: 𐅄 𐅅 𐅆 𐅇. Numbers are written largest first and simply added, so 327 is ΗΗΗΔΔ𐅃ΙΙ. Since four of the six basic signs are ordinary letters, Unicode encodes only the five-signs and the money forms; type Ι Δ Η Χ Μ as Greek letters, not as Latin I, H, X, M.

Athenian accounts counted money, and the same signs changed shape for it: 𐅂 is one drachma, 𐅁 and 𐅀 are half and quarter (an obol was a sixth of a drachma, written with plain Ι), while talents and staters carried a small Τ or Σ: 𐅈 five talents, 𐅋 a hundred talents, 𐅕 ten thousand staters. Other cities had their own letters for the same idea, because their number words began differently; the second grid lists the signs of Thespiae (𐅙 one, 𐅱 a thousand), Troezen (𐅟 five), Hermione, Epidaurus, Messenia, Cyrene, Carystus and Naxos, and one Argive measure of land, the plethron 𐅘.

From the 3rd century BC the alphabetic (Ionic or Milesian) numerals took over and they are still the Greek way of writing ordinals today, on the names of kings and in chapter numbers. The 24 letters plus three old ones give 27 signs: α to θ are 1 to 9, ι to ϟ are 10 to 90, ρ to ϡ are 100 to 900; ϛ stigma stands for 6 (it replaced the letter digamma), ϟ koppa for 90 and ϡ sampi for 900. A keraia ʹ after the last letter marks the group as a number, and a lower keraia ͵ in front multiplies by a thousand: 2026 is ͵βκϛʹ, and the number of the beast, 666, is χξϛʹ. The letters themselves are in Greek Letters; this page holds the three extra ones and both keraias.

The last Greek group comes from papyri and Byzantine documents rather than stone. Scribes in Egypt had shorthand for the talent 𐅺, the drachma 𐅻 and one to five obols 𐅼 𐅽 𐅾 𐅿 𐆀, for measures of wine, oil, grain and land (𐆁 metretes, 𐆂 kyathos, 𐆃 litra, 𐆄 ounkia, 𐆅 xestes, 𐆆 artabe, 𐆇 aroura, 𐆈 gramma, 𐆉 tryblion), for fractions 𐆋 ¼, 𐅵 ½, 𐅷 ⅔, 𐅸 ¾, and for the word 'year' in dates, 𐅹. The zero sign 𐆊 is the one Greek astronomers used in their sexagesimal tables, centuries before the Indian zero reached Europe. 𐆍 marks the indiction, the 15-year tax cycle Byzantine documents are dated by, and 𐆎 the nomisma, the Byzantine gold coin.

Counting rods, Mayan numerals and Kaktovik numerals: place value without Arabic digits

Chinese counting rods were real bamboo or bone sticks laid on a board, and Chinese mathematicians calculated with them from the Warring States period (about the 5th century BC) until the abacus displaced them in the 16th century. Written down, 1 to 5 are that many strokes and 6 to 9 add one stroke at a right angle worth five: 𝍥 is 6. The rule from the Sunzi Suanjing is 'ones vertical, tens horizontal', alternating so that neighbouring digits never merge: units, hundreds and ten-thousands use the upright forms 𝍠 to 𝍨, tens and thousands the flat forms 𝍩 to 𝍱. So 1,234 is 𝍩𝍡𝍫𝍣. Zero was an empty space on the board; from the 13th century it was written 〇. Negative numbers used black rods against red ones for positives, and in writing a slash through the last digit. Japan kept rod numerals as a notation for algebra after China had moved on. Next to them in the same Unicode block are the tally marks: 𝍲 𝍳 𝍴 𝍵 𝍶 build the character 正 one stroke at a time, the way votes and scores are counted in China, Japan, Korea and Taiwan, and 𝍷 𝍸 are the Western one-stroke and five-bar-gate tallies.

Mayan numerals need only three signs: a dot for 1, a bar for 5 and a shell for 0, 𝋠. Within a place they add up to 19, 𝋧 is two dots over a bar, 7, and 𝋳 is four dots over three bars, 19. Larger numbers are stacked vertically in powers of 20: 2026 is 𝋥 over 𝋡 over 𝋦, that is 5 × 400 + 1 × 20 + 6. In the Long Count calendar the third place is worth 360 rather than 400, so 𝋡 𝋠 𝋠 as a date is 360 days, close to a year; the earliest surviving Long Count date is from 36 BC. Unicode encodes the twenty bar-and-dot digits (11.0, 2018), mainly so that Long Count dates can be written; in running text they sit side by side, so write the biggest place first. The carved portrait-head variants of the digits are not encoded.

Kaktovik numerals are the youngest system here and the only one made by children. In 1994 middle-school students at Harold Kaveolook School in Kaktovik, Alaska, working with their teacher William Bartley, found that Arabic digits did not fit Iñupiaq, which counts in twenties like all Inuit languages, and designed a base-20 digit set with a sub-base of five: the strokes on top count fives, the strokes underneath count ones, so 𝋅 is 5, 𝋊 is 10 and 𝋓 is 19, and the zero 𝋀 looks like a pair of crossed arms. The shapes make long division visible as a drawing, and the school reported its pupils' maths scores rising. Unicode added the twenty digits in version 15.0 (2022). Like Mayan numerals they are positional in twenties: 2026 is 𝋅𝋁𝋆. The two sets look alike but are not interchangeable: a Mayan 𝋡 is a dot, a Kaktovik 𝋁 a stroke.

Siyaq, Rumi, Coptic Epact and Sinhala: the accountants' numerals

Siyaq (Ottoman siyakat) is the bookkeepers' numeral system of the Persian and Turkish worlds: not digits but stylised, abbreviated Arabic number words, written right to left, one sign for each unit, ten, hundred, thousand and ten-thousand, added together from the biggest unit down, with no zero. Unicode has two sets. Indic Siyaq (11.0, 2018) is the form used for accounting in Mughal India from the 17th century into the mid-20th: 𞱱 one, 𞱺 ten, 𞲃 a hundred, 𞲌 a thousand, 𞲕 ten thousand, then the Indian units lakh 𞲞 (100,000) and karor 𞲡 (10,000,000) with their plurals 𞲟 and 𞲢, the prefixed units 𞲣 to 𞲫 that are written in front of them, a placeholder 𞲬, the rupee mark 𞲰 and the fractions 𞲭 ¼, 𞲮 ½, 𞲯 ¾. Ottoman Siyaq (12.0, 2019) is the version of the Ottoman treasury's registers, used for centuries until the early 20th: the same units, tens, hundreds, thousands and ten-thousands 𞴁 𞴊 𞴓 𞴜 𞴥, a multiplier 𞴮 marratan ('times') for millions, alternate shapes of several signs, and the fractions 𞴼 ½ and 𞴽 ⅙. The two sets were encoded separately because the shapes diverged.

Rumi numerals, also called Fez numerals, were used in North Africa and al-Andalus from the 10th to the 17th century, above all in the administration of Fez. 'Rumi' means Roman, in the sense of Byzantine, because the signs descend from the Greek and Coptic alphabetic numerals; the system is ciphered, 𐹠 to 𐹨 for 1 to 9, 𐹩 to 𐹱 for the tens, 𐹲 to 𐹺 for the hundreds, with fractions 𐹼 ¼, 𐹽 ⅓, 𐹻 ½ and 𐹾 ⅔. Unicode encoded them in 5.2 (2009).

Coptic Epact numbers are the same Greek numerals in a fast cursive hand. They appear in Coptic documents from about the 8th century and, from the 10th, in the Arabic and Judaeo-Arabic account books of Egypt, where Christians, Muslims and Jews all used them; scholars of the Cairo Geniza now call them zimām numerals, 'ledger letters'. The epact of the name is the Greek word for 'imported'. There are signs for 1 to 9, 10 to 90 and 100 to 900 and no zero; a thousands mark 𐋠 is a combining sign placed on a digit, 𐋡𐋠 for 1,000, and two of them make millions. Unicode added the block in 7.0 (2014) together with the Sinhala archaic numbers, the Sinhala Illakkam of Sri Lanka: 𑇡 to 𑇩 for 1 to 9, 𑇪 to 𑇲 for the tens, 𑇳 a hundred and 𑇴 a thousand, written additively without a zero. They numbered the clauses of the 1815 Kandyan Convention and were out of everyday use by the 1890s; the Sinhala alphabet also has a separate zero-based set, the lith digits, used for astrology.

The North Indic fractions are not a number system but the marks every trader in north India, Pakistan and Nepal added to Devanagari, Gujarati, Gurmukhi or Kaithi ledgers. A rupee was 16 annas, so the fractions are sixteenths: ꠳ 1/16 (one anna), ꠴ ⅛, ꠵ 3/16, ꠰ ¼, ꠱ ½, ꠲ ¾, with the rupee mark ꠸ written before an amount, a placeholder ꠷, a quarter mark ꠶ and a quantity mark ꠹. Unicode put them in a shared block, Common Indic Number Forms (5.2, 2009), precisely because so many scripts used them.

How to copy, type and display ancient number symbols

Tap a sign to copy it. On a computer, Noto Sans Symbols 2 (free, from Google) draws the Attic and papyri Greek signs, the counting rods and tally marks, the Rumi, Coptic Epact and Mayan numerals, and in current builds the Kaktovik numerals; Mayan numerals also have their own Noto Sans Mayan Numerals, the two Siyaq sets need Noto Sans Indic Siyaq Numbers and Noto Serif Ottoman Siyaq, Sinhala archaic numbers come with Noto Sans Sinhala, and the North Indic forms are in Noto Sans Devanagari, Gujarati and the other Indian Noto fonts. Without those fonts a sign shows as a box or a question mark, and most phones ship none of them, so a post with Mayan numerals reads as boxes to most of its readers. The alphabetic Greek numerals Ϛ Ϟ Ϡ are the exception: every Greek-capable font has them.

In Microsoft Word type the code and press Alt+X: 1D2E5 Alt+X gives 𝋥, 10144 Alt+X gives 𐅄. On macOS use the Character Viewer and search by the Unicode name (Mayan Numeral Five, Counting Rod Unit Digit One). In HTML, 𝋥 is 𝋥. Everything here except the Greek letters, the keraias, 〇 and the North Indic forms is above U+FFFF, so some older databases and form fields that count UTF-16 units will refuse or break them.

Three pitfalls. The keraia is its own character, U+0374; the apostrophe, the prime ′ and the modifier letter ʹ U+02B9 look the same and search the same but are not what Greek text uses, and ͵ U+0375 is the lower one. Attic Ι Δ Η Χ Μ must be the Greek letters; Latin look-alikes break search and screen readers. Siyaq numbers are right-to-left Arabic-script characters, so in a left-to-right sentence they order themselves from the right as they should; Mayan and Kaktovik numerals are left-to-right and, in text, lose the vertical stacking they had on stone, so state the place values or write the biggest place first. The Coptic thousands mark 𐋠 is combining: paste it after a digit, never alone.