MesoCalc is a **Mesopotamian calculator**. It
computes in sexagesimal place-value
notation, operates on measures and converts
dates.

MesoCalc was created in March 2013
by Baptiste MÉLÈS
(CNRS, Archives Henri Poincaré, Université de Lorraine) with
the scientific assistance of **Christine PROUST**
(CNRS, Université Paris-Diderot) in the framework of
the SAW Project
(Mathematical Sciences in the Ancient World), headed
by **Karine CHEMLA** (CNRS, Université
Paris-Diderot).

MesoCalc includes computations made by **Mathieu OSSENDRIJVER**
(Humboldt-Universität) and a calendar designed by **Bruno GOMBERT** (Université Paris 1 Panthéon Sorbonne, ARSCAN),
with their benevolent acceptance.

- Introduction
- Arithmetics
- Conversion and arithmetical properties: conversions between decimal and sexagesimal numbers, regularity test, regular approximations, list of regular numbers, prime factors, greatest common divisor;
- Multiplicative operations: multiplication, quotient, reciprocals, tables...
- Exponential operations: square, square root, cube, cube root, geometric progression, tables...
- Additive operations: addition, subtraction;

- Measures
- Lengths, surfaces, volumes, capacities and weights: addition, subtraction, multiplication.

- Dates
- About MesoCalc

The numbers if the calculator below may belong to different kinds:

Code | Numerical system | Examples |
---|---|---|

10A | Decimal place-value notation | 7200 |

60A/F | Sexagesimal place-value notation | 2.0.0 or 2 |

60A | Absolute sexagesimal place-value notation | 2.0.0 |

60F | Floating sexagesimal place-value notation | 2 |

60R | Regular number in 60F | 2 |

Units of length:

danna | ← 30 ← | uš | ← 60 ← | ninda | ← 12 ← | kuš | ← 30 ← | šusi |

10.8 km | 360 m | 6 m | 50 cm | 17 mm |

Units of surface:

gan |
← 100 ← | sar |
← 60 ← | gin |
← 180 ← | še |

3600 m² | 36 m² | 0.6 m² | 33 cm² | |||

1 ninda × 1 ninda |

Units of volume:

gan |
← 100 ← | sar |
← 60 ← | gin |
← 180 ← | še |

1800 m³ | 18 m³ | 300 dm³ | 1.66 dm³ | |||

1 (surface-)sar × 1 kuš |

Units of capacity:

gur |
← 5 ← | bariga |
← 6 ← | ban |
← 10 ← | sila |
← 60 ← | gin |
← 180 ← | še |

300 L | 60 L | 10 L | 1 L | 16.6 mL | 0.092 mL |

Units of weight:

gu |
← 60 ← | mana |
← 60 ← | gin |
← 180 ← | še |

30 kg | 500 g | 8.33 g | 0.046 g |

System G:

šar-gal |
← 6 ← | šar'u |
← 10 ← | šar |
← 6 ← | bur'u |
← 10 ← | bur |
← 3 ← | eše |
← 6 ← | iku |

64800 | 10800 | 1080 | 180 | 18 | 6 | 1 |

System S:

šar-gal |
← 6 ← | šar'u |
← 10 ← | šar |
← 6 ← | gešu |
← 10 ← | geš |
← 6 ← | u |
← 10 ← | diš |

216000 | 36000 | 3600 | 600 | 60 | 10 | 1 |

During the Neo Babylonian and Persian periods, which
are concerned by this converter, the year was based on the
revolution of the Earth around the Sun, that is 365 days. It
was beginning in spring, during the Babylonian month of
*nisannu* (1), and ending during month *addaru*
(12). Years’ calculation was based on Kings’ reigns which are
well known, thanks to *Ptolemy's Canon*. This
fundamental document allows us establishing equivalences
between Babylonian and Gregorian dates.

The year in which a king acceded to the throne, is recorded as “Year 0” in this converter, then subsequent regnal years are numbered until the next King. A year consisted of 12 lunar months, each of them corresponding to the interval between two new moons, thus 12 × 29 or 30 days :

- 1:
*nisannu* - 2:
*aiāru* - 3:
*simānu* - 4:
*dūzu* - 5:
*abu* - 6:
*ulūlu* - 7:
*tašrītu* - 8:
*arahsamnu* - 9:
*kislīmu* - 10:
*ṭebētu* - 11:
*šabāṭu* - 12:
*addaru*

However, 11 days are lacking to complete the solar year. To fill this gap, Mesopotamians used empirically to add from time to time a 13th month. This intercalary month was added either after the 6th (month 6b), or the 12th (month 12b).

A mathematical scheme enabling a regular cycle of intercalary
months was elaborated during Achaemenid Period, based on the
fact that 19 solar years and 235 lunar months have the same
number of days. Seven intercalary months were added over a
period of 19 years, on year 1, 3, 6, 9, 11, 14, and 17 year.
Only the 1st year had an intercalary month *ulūlu* (6b), all the
others had an *addaru* (12b).

Chronological equivalences between Babylonian and Gregorian dates of
this converter have been taken from the book of R. A. Parker and
W. H. Dubberstein, *Babylonian Chronology, 626 B.C. - A.D. 45*,
Studies in Ancient Oriental Civilization 24, 1942 and encoded by Bruno
Gombert (Université Paris 1 Panthéon Sorbonne, ARSCAN).

Yes, you can! To download MesoCalc and use it offline on your computer or smartphone,

- either right-click on the present link and select "Save As";
- or select "File > Save As" in your web browser while it is displaying the present page.

Yes, you can! MesoCalc is a free software. You can read the source code of the present web page. You can even modify the source code and then redistribute your own modifications under the terms of the GNU General Public License (see the license below).

If you want to see the HTML, CSS and JavaScript source code of this program, you will have to find on option like "View > Page Source" or "Tools > Source Code" in your web browser while displaying the present web page.

Yes, it is. Archiving software is crucial because programmers are not aware that this part of scientific culture disappears more easily than clay tablets. The programs and source codes of the first decades of computer science are already lost at the beginning of the XXIth century.

This is the reason why MesoCalc'c source code is archived. You can find its successive versions (since 2016) on https://github.com/BapMel/mesocalc.

Yes, very frequently! Month after month, MesoCalc gets new features and new bug corrections. In case you downloaded MesoCalc to use it offline, make sure that you have the newest version.

Last modifications:

**16th September 2015:**bug correction in measurement units. Now, input numbers can be either decimal or sexagesimal (until recently, only sexagesimal numbers were accepted).**15th January 2016:**two new features. 1) Regular approximation of a number; 2) a new algorithm to list regular numbers, made possible by Mathieu Ossendrijver's huge database of regular numbers.**7th May 2016:**metric approximation of measuring units (metres, litres, etc.). Bug correction in system G (1 šar-gal = 64800, not 34800). Cleaning of the HTML code. "Clear" buttons for all operations on measuring units. Verification of the XHTML 1.0 Strict validity :**16th May 2017:**integration of Bruno Gombert's calendar, designed after R. A. Parker and W. H. Dubberstein,*Babylonian Chronology, 626 B.C.-A.D. 45*, Studies in Ancient Oriental Civilization 24, 1942.

MesoCalc: a Mesopotamian calculator.

Copyright (C) Baptiste MÉLÈS 2013.

Latest version: 19th May 2017.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

If you see bugs or want new features, please contact Baptiste Mélès. All comments and suggestions are welcome!