List of numeral systems

There are many different numeral systems, that is, writing systems for expressing numbers.

By culture / time period

"A base is a natural number B whose powers are specially designated within a numerical system." The term is not equivalent to radix, as it applies to all numerical notation systems and most systems of spoken numbers. Some systems have two bases, a smaller and a larger ; an example is Roman numerals, which are organized by fives and tens.

Name	Base	Sample	Approx. First Appearance
Proto-cuneiform numerals	1060
Indus numerals	unknown
Proto-Elamite numerals	1060
Sumerian numerals	1060
Egyptian numerals	10	Z1 V20 V1 M12 D50 I8 I7 C11
Babylonian numerals	1060
Aegean numerals	10	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Chinese numerals Japanese numerals Korean numerals Vietnamese numerals	10	零一二三四五六七八九十百千萬億〇一二三四五六七八九十百千万亿
Roman numerals	510	I V X L C D M
Hebrew numerals	10
Indian numerals	10	Bengali ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ৯ Devanagari ० १ २ ३ ४ ५ ६ ७ ८ ९ Gujarati ૦ ૧ ૨ ૩ ૪ ૫ ૬ ૭ ૮ ૯ Kannada ೦ ೧ ೨ ೩ ೪ ೫ ೬ ೭ ೮ ೯ Malayalam ൦ ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯ Odia ୦ ୧ ୨ ୩ ୪ ୫ ୬ ୭ ୮ ୯ Punjabi ੦ ੧ ੨ ੩ ੪ ੫ ੬ ੭ ੮ ੯ Tamil ௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯ Telugu ౦ ౧ ౨ ౩ ౪ ౫ ౬ ౭ ౮ ౯ Tibetan ༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩ Urdu ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹
Greek numerals	10	ō α β γ δ ε ϝ ζ η θ ι ο Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ
Kharosthi numerals	410	? ? ? ? ? ? ? ?
Phoenician numerals	10	? ? ? ??? ??? ??? ?? ?? ?? ? ? ?
Chinese rod numerals	10	? ? ? ? ? ? ? ? ? ?
Coptic numerals	10	Ⲁ Ⲃ Ⲅ Ⲇ Ⲉ Ⲋ Ⲍ Ⲏ Ⲑ
Ge'ez numerals	10	፩ ፪ ፫ ፬ ፭ ፮ ፯ ፰ ፱ ፲ ፳ ፴ ፵ ፶ ፷ ፸ ፹ ፺ ፻ ፼	15th Century
Armenian numerals	10	Ա Բ Գ Դ Ե Զ Է Ը Թ Ժ
Khmer numerals	10	០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩
Thai numerals	10	๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙
Abjad numerals	10	غ ظ ض ذ خ ث ت ش ر ق ص ف ع س ن م ل ك ي ط ح ز و هـ د ج ب ا
Chinese numerals	10	零壹貳參肆伍陸柒捌玖拾佰仟萬億零壹贰叁肆伍陆柒捌玖拾佰仟萬億
Eastern Arabic numerals	10	٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠
Vietnamese numerals	10	? ? ? ? ? ? ? ? ?
Western Arabic numerals	10	0 1 2 3 4 5 6 7 8 9
Glagolitic numerals	10	Ⰰ Ⰱ Ⰲ Ⰳ Ⰴ Ⰵ Ⰶ Ⰷ Ⰸ...
Cyrillic numerals	10	а в г д е ѕ з и ѳ і...
Rumi numerals	10
Burmese numerals	10	၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉
Tangut numerals	10
Cistercian numerals	10
Maya numerals	520	15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px 15px ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Muisca numerals	20
Korean numerals	10	영 일 이 삼 사 오 육 칠 팔 구
Aztec numerals	20	x25px x25px x25px x25px x25px x25px x30px
Sinhala numerals	10	෦ ෧ ෨ ෩ ෪ ෫ ෬ ෭ ෮ ෯ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Pentadic runes	10
Cherokee numerals	10
Vai numerals	10	꘠ ꘡ ꘢ ꘣ ꘤ ꘥ ꘦ ꘧ ꘨ ꘩
Bamum numerals	10	ꛯ ꛦ ꛧ ꛨ ꛩ ꛪ ꛫ ꛬ ꛭ ꛮ
Mende Kikakui numerals	10	? ? ? ? ? ? ? ? ?
Osmanya numerals	10	? ? ? ? ? ? ? ? ? ?
Medefaidrin numerals	20	? ?/? ?/? ?/? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
N'Ko numerals	10	߉ ߈ ߇ ߆ ߅ ߄ ߃ ߂ ߁ ߀
Hmong numerals	10
Garay numerals	10
Adlam numerals	10	? ? ? ? ? ? ? ? ? ?
Kaktovik numerals	520	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Sundanese numerals	10	᮰ ᮱ ᮲ ᮳ ᮴ ᮵ ᮶ ᮷ ᮸ ᮹	20th Century

By type of notation

Numeral systems are classified here as to whether they use positional notation, and further categorized by radix or base.

Standard positional numeral systems

The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation.

Base	Name	Usage
2	Binary	Digital computing, imperial and customary volume
3	Ternary, trinary	Cantor set ; counting Tasbih in Islam; hand-foot-yard and teaspoon-tablespoon-shot measurement systems; most economical integer base
4	Quaternary	Chumashan languages and Kharosthi numerals
5	Quinary	Gumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6	Senary, seximal	Diceware, Ndom, Kanum, and Proto-Uralic language
7	Septimal, Septenary
8	Octal	Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, Yuki, Pame, compact notation for binary numbers, Xiantian
9	Nonary, nonal	Compact notation for ternary
10	Decimal, denary	Most widely used by contemporary societies
11	Undecimal, unodecimal, undenary	A base-11 number system was mistakenly attributed to the Māori in the 19th century and one was reported to be used by the Pangwa in the 20th century, but was not confirmed by later research and is believed to also be an error. Briefly proposed during the French Revolution to settle a dispute between those proposing a shift to duodecimal and those who were content with decimal. Used as a check digit in ISBN for 10-digit ISBNs. Applications in computer science and technology.
12	Duodecimal, dozenal	Languages in the Nigerian Middle Belt Janji, Gbiri-Niragu, Piti, and the Nimbia dialect of Gwandara; Chepang language of Nepal, and the Mahl dialect of Maldivian; dozen-gross-great gross counting; 12-hour clock and months timekeeping; years of Chinese zodiac; foot and inch; Roman fractions.
13	Tredecimal, tridecimal	Conway's base 13 function.
14	Quattuordecimal, quadrodecimal	Programming for the HP 9100A/B calculator and image processing applications.
15	Quindecimal, pentadecimal	Telephony routing over IP, and the Huli language.
16	Hexadecimal, sexadecimal, sedecimal	Compact notation for binary data; tonal system of Nystrom.
17	Heptadecimal, septendecimal
18	Octodecimal
19	Undevicesimal, nonadecimal
20	Vigesimal	Basque, Celtic, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages.
5&20	Quinary-vigesimal	Greenlandic, Iñupiaq, Kaktovik, Maya, Nunivak Cupʼig, and Yupʼik numerals – "wide-spread... in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon"
21		The smallest base in which all fractions to have periods of 4 or shorter.
23		Kalam language,
24	Quadravigesimal	24-hour clock timekeeping; Greek alphabet; Kaugel language.
25		Sometimes used as compact notation for quinary.
26	Hexavigesimal	Sometimes used for encryption or ciphering, using all letters in the English alphabet
27		Telefol, Oksapmin, Wambon, and Hewa languages. Mapping the nonzero digits to the alphabet and zero to the space is occasionally used to provide checksums for alphabetic data such as personal names, to provide a concise encoding of alphabetic strings, or as the basis for a form of gematria. Compact notation for ternary.
28		Months timekeeping.
30		The Natural Area Code, this is the smallest base such that all of to terminate, a number n is a regular number if and only if terminates in base 30.
32	Duotrigesimal	Found in the Ngiti language.
34		The smallest base where terminates and all of to have periods of 4 or shorter.
36	Hexatrigesimal
40		DEC RADIX 50/MOD40 encoding used to compactly represent file names and other symbols on Digital Equipment Corporation computers. The character set is a subset of ASCII consisting of space, upper case letters, the punctuation marks "$", ".", and "%", and the numerals.
42		Largest base for which all minimal primes are known.
47		Smallest base for which no generalized Wieferich primes are known.
49		Compact notation for septenary.
50		SQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits.
60	Sexagesimal	Babylonian numerals and Sumerian; degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari; covers base 62 apart from I, O, and l, but including _.
64
72		The smallest base greater than binary such that no three-digit narcissistic number exists.
80		Used as a sub-base in Supyire.
89		Largest base for which all left-truncatable primes are known.
90		Related to Goormaghtigh conjecture for the generalized repunit numbers.
97		Smallest base which is not perfect odd power for which no generalized Wagstaff primes are known.
185		Smallest base which is not a perfect power for which no generalized repunit primes are known.
210		Smallest base such that all fractions to terminate.