"The chamber dimensions are rather variable, particularly in the Subterranean and Antechamber, and none of the above data are equal in quality to the King's Chamber dimensions. If a strictly weighted mean be taken it yields 20.620 ± 004; but taking the King's Chamber alone, as being the best datum by far, it nevertheless contracts upwards, so that it is hardly justifiable to adopt a larger result than 20.620 ± .005."
- Flinders Petrie1
The length of the cubit varied only slightly throughout the land and history of Ancient Egypt. Originally based on the length of the fore arm, and written hieroglyphically as such, it was also expressed as 28 fingers or 7 palms. The length of extant funerary cubit sticks varies from 523mm to 538.7mm and it is likely that the cubit used in the construction of one building differed slightly in length from that used in another building. The cubit that was used in the construction of the Great Pyramid has never been found and it is only from taking many measurements of the building that its length can be known. Both Flinders Petrie and Rudolf Gantenbrink agree that a cubit of 523.6 mm, or 20.62 inches was used in planning and construction of Khufu's tomb.
In his paper Ascertaining and evaluating relevant structural points using the Cheops Pyramid as an example, Rudolf Gantenbrink suggests that before an evaluation of the measurements can be undertaken, which he believes should be based on whole-number values and ratios, the points of special importance within the structure must be determined.
"A clearly defined, common reference point for all three structures lies in the height of the corridor ceilings. On the floor, however, there is no defined conclusion, either for the Great Gallery nor for the other galleries. Here, too, the corridors, or their theoretical extension, do not have the same heights, so that here no conclusion is possible at the angle bisects, either. A further indication that the ceiling height was very probably a primary construction quantity is evident from the Cheops Pyramid's rock chambers (the 'Relieving Chambers' situated above the King's chamber). The ceilings are the only completed element of these chambers, a finding which occurs also in other rock chambers of the Old Kingdom. The walls and floor, on the other hand, are still in unfinished state and cannot therefore possibly have served as a reference for measurements
These indices point to the fact that the primary construction points must generally be looked for at the ceilings and not on the floors, which hitherto have simply been regarded as a reference height for no good reason."
- Rudolf Gantenbrink.
If this method of analysis is applied to the ceilings of the chambers it is revealed that their positions are related, and can be expressed, by whole-number values and ratios. The measures used here are based upon the detailed measurements recorded by Flinders Petrie and published in his Pyramids and Temples of Gizeh.
The figure of Osiris-Djed visible in the pyramid's design does not stand level with the base of the pyramid. Instead, he appears as though half buried, rising out of the mound of bedrock upon which the pyramid was built. The measurements and ratios of the chamber's ceilings shown in the table below are therefore taken, not from the pyramid's base, but from the floor of the passage leading to the Subterranean chamber. The floor of the passage is used as a base rather than the floor of the chamber as the latter is rough and irregular making it impossible to base any reliable measurements upon. The pit that has been dug in the floor of that chamber by early explorers, being unrelated to the original design, is therefore not included in the measurements. This floor upon which the colossal figure of Osiris-Djed stands at the bottom of the entrance passage was measured by Flinders Petrie as 1181 inches or 57.27 cubits below the pavement of the pyramid.
The table below summarizes the heights of the chambers according to the measurements taken by Petrie:
Location within the pyramid Height above Subterranean passage floor Campbell's chamber apex 179.72 cubits?
3706 inches? (1181 + 2525?) P&T 21:148
King's chamber ceiling 150.51 cubits
3103.6 inches (1181 + 1922.6) P&T 7:55
Queen's chamber apex 109.62 cubits
2260.5 inches (1181 + 1079.5) P&T 7:40, 7:41
Pyramid's entrance ceiling 91.5 cubits
1886.9 inches (1181 + 705.97) P&T 6:32
Reduced to whole-number values and ratios the measurements of the pyramid can be expressed as follows:
Internal chamber system with the position of key points in whole-number values and ratios.
The measurements rounded to whole-number values in the diagram above vary only slightly from those made by Petrie, who himself expressed the difficulty of accurately measuring the heights of the chambers. The small chambers situated above the King's chamber would be particularly difficult to measure the height of and for the apex of Campbell's chamber he relies on the measurements taken by Vyse. The pyramid's entrance height is notably not a round figure when measured in cubits. Expressed as a ratio of the King's chamber height above the subterranean passage, however, it could be described as being 11/18 of that height. 2
The position of the King's chamber features compared with those of the Queen's chamber are found to be of the same 11:18 relationship. (Click here to see them compared)
The reoccurrence of the 11/18 ratio and its significance will be discussed in more depth in the following page.
Canon of Proportions
1. Pyramids and Temples of Gizeh, 20:136.
2. This calculation would place the pyramid's entrance at 91.66 cubits above the subterranean passage floor - within less than three inches of Petrie's measurement of 91.5 cubits. If we instead adhere strictly to the measurements recorded by Petrie then then entrance height is calculated as 10.98 /18 of the King's chamber height.
The Concept of the Pyramid
Canon of Proportions
The Pyramid and the Body