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Babylonian Numerals

Tool to convert babylonian numbers (Babylonian Numerals). The Mesopotamian numeral system uses a mix of base 60 (sexagesimal) and base 10 (decimal) by writing wedges (vertical or corner wedge).

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Babylonian Numerals -

Tag(s) : Numeral System, History, Symbol Substitution

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Babylonian Numerals

Babylonian to Hindu-Arabic Numbers Converter

Hindu-Arabic to Babylonian Numbers Converter






Tool to convert babylonian numbers (Babylonian Numerals). The Mesopotamian numeral system uses a mix of base 60 (sexagesimal) and base 10 (decimal) by writing wedges (vertical or corner wedge).

Answers to Questions

How to write babylonian numbers?

In mesopotamian/babylonian number system, numbers have to be converted to base 60. Numbers are written in a cuneiform style with | and <. Each vertical bar | (pipe) equals a unit and each < (corner wedge or bracket) equals a tenth. The change of power of sixty (60 ^ 1 = 60, 60 ^ 2 = 3600, 30 ^ 3 = 216000, etc.) is represented by a space.

Example: 23 is written with 2 tenthes and 3 units so <<||| or char(66)char(51)

Example: 61 is written 1 sixtieth and 1 unit as | | or char(49)char(49) (with a space separator)

dCode uses the recent system (from the 3rd century civilization in Babylon) which introduce the writing or 0 (before the concept of zero did not exist, it was replace by an ambiguous empty space).

Since Unicode 5 (2006) cuneiform symbols can be represented on compatible browsers, here is the table of characters used by dCode:

𒐕1𒐖2𒐗3𒐘4𒐙5𒐚6𒐛7
𒐜8𒐝9𒌋10𒎙20𒌍30𒐏40𒐐50
NB: The double chevron character 𒎙 (20) has been forgotten in Unicode 5 and added in Unicode 8 (2015) but may appear malformed on some operating systems.

How to convert babylonian numbers?

Converting is easy by counting symbols and considering it in base 60.

Example: <<||| is 2 < and 3 | so $ 2 \times 10 + 3 \times 1 = 23 $

Example: | | (note the space) is 1 | and then 1 | so $ 1 \times 60 + 1 = 61 $

How to convert from base 10 to base 60?

TO convert a number $ n $ from base $ 10 $ to base $ b=60 $ apply the algorithm:

$$ q_0=n; i=0; \mbox{ while } q_i > 0 \mbox{ do } (r_i = q_i \mbox{ mod } 60; q_{i+1}= q_i \mbox{ div } 60 ; i = i+1 ) $$

Example: $$ q_0 = 100 \\ r_0 = 100 \mbox{ mod } 60 = 40 \;\;\; q_1 = 100 \mbox{ div } 60 = 1 \\ r_1 = 1 \mbox{ mod } 60 = 1 \;\;\; q_2 = 0 \\ So \{1,0,0\}_{(10)} = \{1, 40\}_{(60)}

How to write the number zero 0?

Babylonnians did not use the zero (this concept had not been invented), but from the 3rd century they used the symbol char(48)

How to count using babylonian numerals?

Babylonian numbers chart (base60)

0 (zero)char(48)1char(49)2char(50)3char(51)4char(52)
5char(53)6char(54)7char(55)8char(56)9char(57)
10char(65)11char(65)char(49)12char(65)char(50)13char(65)char(51)14char(65)char(52)
15char(65)char(53)16char(65)char(54)17char(65)char(55)18char(65)char(56)19char(65)char(57)
20char(66)21char(66)char(49)22char(66)char(50)23char(66)char(51)24char(66)char(52)
25char(66)char(53)26char(66)char(54)27char(66)char(55)28char(66)char(56)29char(66)char(57)
30char(67)31char(67)char(49)32char(67)char(50)33char(67)char(51)34char(67)char(52)
35char(67)char(53)36char(67)char(54)37char(67)char(55)38char(67)char(56)39char(67)char(57)
40char(68)41char(68)char(49)42char(68)char(50)43char(68)char(51)44char(68)char(52)
45char(68)char(53)46char(68)char(54)47char(68)char(55)48char(68)char(56)49char(68)char(57)
50char(69)51char(69)char(49)52char(69)char(50)53char(69)char(51)54char(69)char(52)
55char(69)char(53)56char(69)char(54)57char(69)char(55)58char(69)char(56)59char(69)char(57)

For other numbers, use the form above.

Why the base 60?

60 has the advantage of having many divisors.

Today the time system of hours still uses the base sixty: 60 seconds = 1 minute, 60 minutes = 1 hour = 3600 seconds

How to convert babylonian numbers into roman numerals?

Convert the babylonian numbers to Hindu-Arabic numerals (1,2,3,4,5,6,7,8,9,0), then use the Roman numeral converter of dCode.

Source code

dCode retains ownership of the source code of the script Babylonian Numerals online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Babylonian Numerals script for offline use on PC, iPhone or Android, ask for price quote on contact page !

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Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Babylonian Numerals tool. Thank you.


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