Greek numerals

Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Milesian numerals, Alexandrian numerals, or alphabetic numerals. In modern Greece, they are still in use for ordinal numbers, and in much of the same way that Roman numerals are in the West; for ordinary (cardinal) numbers, Arabic numerals are used.

Numeral systems by culture
Hindu–Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou Counting rods	Japanese Korean
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Greek (Ionian) Āryabhaṭa
Other systems
Attic Babylonian Egyptian Etruscan	Mayan Roman Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…

At first, before it was used more, the Greek alphabet, Linear A and Linear B had used a different system with symbols for 1, 10, 100, 1000 and 10000 operating with the following formula: | = 1, – = 10, ◦ = 100, ¤ = 1000, ☼ = 10000.

The earliest alphabet-related system of numerals used with the Greek letters was a set of the acrophonic Attic numerals, operating much like Roman numerals (which derived from this scheme), with the following formula: Ι = 1, Γ = 5, Δ = 10, ΓΔ = 50, Η = 100, ΓΗ = 500, Χ = 1000, ΓΧ = 5000, Μ = 10000 and ΓΜ = 50000.

The acrophonic system was replaced by a new alphabetic system, sometimes called the Ionic numeral system, from the 4th century BC. Each unit (1, 2, …, 9) was assigned a separate letter, each tens (10, 20, …, 90) a separate letter, and each hundreds (100, 200, …, 900) a separate letter. This requires 27 letters, so the 24-letter Greek alphabet was extended by using three obsolete letters: fau ϝ, (also used are [Sigma (letter)|sigma] ϛ or, in modern Greek, ΣΤ) for 6, koppa ϟ for 90, and sampi ϡ for 900. To distinguish numerals from letters they are followed by the "keraia" (Greek κεραία—insect antenna), a symbol similar to an acute sign (Unicode U+0374).

Fau (also spelled vau, pronounced wow) may also be called digamma. The two are the same in meaning, and either symbol may be used to represent the number 6.

This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 241 is represented as ΣΜΑʹ (200 + 40 + 1).

To represent numbers from 1,000 to 999,999 the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. A "left keraia" (Unicode U+0375, ‘Greek Lower Numeral Sign’) is put in front of thousands to distinguish.

Ancient	Byzantine	Modern	Value		Ancient	Byzantine	Modern	Value		Ancient	Byzantine	Modern	Value		Ancient	Byzantine	Modern	Value
	α	Αʹ	1			ι	Ιʹ	10			ρ	Ρʹ	100		&	͵α	͵Α	1000
	β	Βʹ	2			κ	Κʹ	20			σ	Σʹ	200			͵β	͵Β	2000
	γ	Γʹ	3			λ	Λʹ	30			τ	Τʹ	300			͵	͵Γ	3000
	δ	Δʹ	4			μ	Μʹ	40			υ	Υʹ	400			͵	͵Δ	4000
	ε	Εʹ	5			ν	Νʹ	50			φ	Φʹ	500			͵ε	͵Ε	5000
	&   &	Ϛʹ ΣΤʹ	6			ξ	Ξʹ	60			χ	Χʹ	600			͵ & ͵ ͵ & ͵	͵Ϛ ͵ΣΤ	6000
	ζ	Ζʹ	7			ο	Οʹ	70			ψ	Ψʹ	700			͵ζ	͵Z	7000
	η	Ηʹ	8			π	Πʹ	80			ω	Ωʹ	800			͵η	͵H	8000
	θ	Θʹ	9			&   &	Ϟʹ	90		&   &	&   &   &	Ϡʹ	900			͵θ	͵Θ	9000

Higher numbers

The Greeks also used the myriad to denote 10,000 (Μʹ) and the myriad myriad for one hundred million (ΜΜʹ).

Decimal	Symbol	Greek numeral
1	Ι	εἷς (eis)
5	Γ	πέντε (pente)
10	Δ	δέκα (deka)
100	Η	ἑκατόν (hekaton)
1000	Χ	χίλιοι (chilioi)
10000	Μ	μύριοι (myrioi)

Greek Numerals Media

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  Acrophonic Attic numeral 50. Based on shape from: Samuel Verdan, Systèmes numéraux en Grèce ancienne (2007).

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  Acrophonic Attic numeral 500. Based on shape from: Samuel Verdan, Systèmes numéraux en Grèce ancienne (2007).

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  Acrophonic Attic numeral 5000. Based on shape from: Samuel Verdan, Systèmes numéraux en Grèce ancienne (2007).

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  Acrophonic Attic numeral 50000. Based on shape from: Samuel Verdan, Systèmes numéraux en Grèce ancienne (2007).

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  Greek numerals in a c. 1100 Byzantine manuscript of Hero of Alexandria's Metrika. The first line contains the number "͵θϡϟϛ δʹ ϛʹ", i.e.

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  A 14th-century Byzantine map of the British Isles from a manuscript of Ptolemy's Geography, using Greek numerals for its graticule: 52–63°N of the equator and 6–33°E from Ptolemy's Prime Meridian at the Fortunate Isles.

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  cursive form of Greek numeral symbol Koppa, after Thompson, Introduction to Greek Palaeography

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  cursive form of Greek numeral symbol Koppa, after Thompson, Introduction to Greek Palaeography

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  Handwritten form of Greek numeral symbol Koppa, from a 10th-century manuscript [1]

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  modern minuscule form of Greek numeral symbol Koppa

Other websites

• The Greek Number Converter