## Basic Egyptian Metrology

Egyptian metrology is quite complicated and does vary over time, although not as much as Mesopotamian metrology.  This list gives the basic units as used either in the Old Kingdom or RMP.  In particular, we take no notice of later changes in units of weights and measures.

### Length

The standard unit of length was the cubit.  The length of the cubit varies, but was around 52.5 cm.
The subdivisions of the cubit were: 1 cubit = 7 palms = 28 digits.
There was also a cubit of 6 palms, but this does not occur in the mathematical exercises.
Larger units were the khet, usually translated as a rod or 'rod of cord' or rope, of 100 cubits (ca 52 m.) and the 'river measure' of 20000 cubits (ca. 10.5 km).  This last unit is presumed to reflect one day's travel towing a boat up the Nile.

### Area

The basic unit of area was the setat, usually translated as 'aroura' from the Greek for 'field', of 100x100 cubits, or 1 rod by 1 rod.  This area is about 2/3 of an acre.  Subunits were given as 1/2, 1/4 or 1/8 of a setat.  Smaller areas were given in terms of strips of land called cubits and measuring 100 cubits (1 khet) in length by 1 cubit in width.  Multiples of the area cubit are obtained by increasing the width, while keeping the length constant.

### Volume

The only known unit of volume is the denit of a cubic cubit.  This was used only to measure the progress of excavations.  In the RMP there are numerous calculations of volumes, but no units are given.

### Slope

Slope, especially of objects like pyramids, was measured in terms of the seked, which gives the length in palms for an increase in height of 1 cubit.  In the Old Kingdom, the most commonly used values were a seked of 5 1/2 or 5 1/4.

### Capacity

Dry capacity: Grain and flour were measured in a system of capacity units.  The basic capacity unit was the hekat, of about 4.8 liters. Fractions of a hekat were denoted in what are called 'Horus eye' fractions.  That is, there are specific notations for 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64 of a hekat.  Apart from the 1/2 hekat sign, these subunits are only known in hieratic until the 19th Dynasty.  It may be that the hieroglyphic versions, and possibly the connection with the accompanying myth, were derived from the hieratic notation.  Quantities smaller than the 1/60 hekat were measured in terms of the ro of 1/320 hekat.

One minor complication is that, in the RMP, there is a larger unit, the khar, composed of 5 quadruple-hekat.  The khar and the quadruple-hekat are considered as units.  Earlier, the khar had been composed of 10 hekat and from Dynasty 18 onwards there is a khar of 4 quadruple-hekat.  The horus eye fractions may refer either to the hekat or to the quadruple-hekat.
The khar provides the link between volume calculations in unnamed units and capacity calculations: the khar is 2/3 a cubic cubit.

Liquid capacity: Fluids, such as beer, milk and honey were measured in terms of a hin of about 0.48 liter (1/10 hekat), divided into 32 parts.  Larger quantities were often measured in 'jars', which could certainly vary in size.

### Baking ratio

An important quantity, often referred to as the 'baking ratio' was the pesu.  This measured the number of loaves or jugs (or hin) of beer that were produced from one hekat (or quadruple-hekat) of grain.  For loaves, this measures size: the greater the pesu, the smaller the loaf.  For beer, it measures strength: the greater the pesu, the weaker the beer.

Up to Day 9

Last modified: 03 October 2005
Duncan J. Melville

Comments to dmelville@stlawu.edu