The present table is a concordance of ancient Egyptian units of measurement which are used throughout the Rhind Mathematical Papyrus, an ancient Egyptian document which is a record of elementary mathematics. The papyrus consists of four sections:
- a title page with historical information,
- a table of fractional calculations for 2/3 - 2/101, or the "2/n table" (where n is always odd),
- a much smaller table of fractional calculations for the nine fractions 1/10 - 9/10, or the "1-9/10" table, and finally
- a series of 91 "problems" or numbers, which are numbered from 1-87 (a modern convention imposed on the document to differentiate the problems) and include four additional items designated by moderns as 7B, 59B, 61B, and 82B.
Many of the latter problems make use of certain ancient Egyptian units of measurement, whether of length, volume, time, or otherwise, and this is what the present table summarizes. It happens that none of the 2/n table, the 1-9/10 table, or even most of the first several problems 7, 7B, 8-34 make any mention of units, and they are therefore not included in this table.
Almost all usage of units of measure is confined to the later problems in the papyrus (with some early exceptions, also listed), being the title page, problems 1-6, and problems 35-87, which include three additional items designated as 59B, 61B, and 82B.
For the title page and numbers 86-87, the context of the usage of units is not mathematical, but historical.
The units are grouped by unit type, and color-coded. From top to bottom, the unit types are:
- length,
- area,
- volume (deben),
- monetary (sha'ty),
- trigonometric (seked),
- food/manufacturing (pefsu), and finally
- "foodstuff" (loaves, des-measure).
The seked is not strictly speaking a trigonometric item, but its context is so close to our modern understanding of trigonometry that we identify it with that word.
The pefsu is also a kind of derived unit of measure relating to food preparation and manufacturing.
Finally, the "loaf' is not really a standard unit of measure within the papyrus as such, but it is mentioned so frequently in related contexts that it merits its own entry. In any one problem, it can be interpreted as a measure of solid food.
Likewise, the "des-measure", mentioned in only a few problems, can be interpreted as a volume unit of liquid measure (especially in the context of food and drink) which is not immediately related to the other volume units.
Entries in black indicate that a given unit of measure is explicitly named or entailed in the problem, in the original document.
Entries in gray indicate that although the unit's word is not expressly stated in that problem, the context of the document makes clear that the unit is implicitly being used in the course of the problem's calculation, statement, etc.
Note that neighboring groups of problems often tend to entail similar units, although in some cases the units are merely strongly implied by context, as opposed to being explicitly stated in the original document.
In the Rhind Papyrus, units of a given type have precise, exact, simple relationships to one another, which conversion factors we can and therefore do easily express in modern terms, using only integers.
Although there is historical evidence that certain units of measure can be "concretely" compared with modern units, these exact specifications are not essential to reading the Rhind Papyrus as a mathematical document.
Indeed, one can read the papyrus has having an internally consistent system of units of measure, which is all that is presented in this table and explanation.
The reader is cautioned that ancient Egypt had a very long history, and that the present information about units pertains directly to the Rhind Papyrus only.
At other periods of ancient Egyptian history, certain units were taken to have different conversion factors relative to other units.
Among units of length, 1 khet = 100 cubits = 700 palms = 2800 fingers.
Among units of area, one square khet is called one setat, and 1 setat = 100 cubit strips, where one cubit strip is a rectangular strip of area being 1 cubit by 100 cubits (or any other sector of equal area).
Among units of volume, the following holds: