Khufu.dk August, 2008. Work in progress and not free of errors!

Dimensions of Pyramid of Khufu (Cheops)
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Outer dimensions

Conversion of English units

From English units to the International System of Units (SI):

1 inch is exact 2.54 cm
1 feet is 12 inch or 0.3048 m
1 yard is 3 feet or 0.9144 m
1 mile is 1 760 yards or 1 609 m or 1.609 kilometers (km)
1 square mile is 2.590 square kilometers (sq.km)
1 acre is 4 047 square meters (sq.m)
1 square feet is 0.0929 sq.m.
1 pund (lb) is 0.4536 kilogram (kg)

Shorts:
inch = "
feet = ft
yard = yd
square mile = sq.mile
pound = lb (unit of weight)

To judge the height and especially the angle of a pyramid by the eye is very difficult. Herodotus
was told that the lenght and the height was the same. Below some suggestions about how it
could be understood.

Baselength 230.348 m or 440 cubits

Baselenghts, Petrie

Measurements of the baselenghts was for a long time a huge problem, because dunes of sand
covered several meters of the sides of the pyramid. It was probably by the Expedition of Napo-
leon in 1799-1801 that sand for the first time was removed down to the corners on the northside
and made an accurate measurement possible. The facit "232,76 mètres" was wrong. And regret-
tably the wrongdoing was repeated in 1837 by Howard Vyse and John Shae Perring, when they
completely freed the northside and achieved 764 feet or 232.9 meter. And confirming the mis-
take by the Expedition of Napoleon.

Flinders Petrie discovered the mistake during his measurements in 1881-82. Before, it was
assumed that the sockets of the four cornerblocks were fully covered by the casingblocks,
but the sockets of the missing cornerblocks were only partly covered. See drawing below.

Baselenghts corrected by Petrie

The sidelenghts had to be reduced and deminished to:

Northside: 9069.4" or 230.363 m.
Southside: 9069.5" or 230.365 m. Longest.
Westside.: 9068.6" or 230.342 m.
Eastside.: 9067.7" or 230.320 m. Shortest.
Mean.....: 9068.8" or 230.348 m.

Biggest difference was 1.8 inch or 4.6 cm between south- and eastside.
See Petrie, Ch. 6, Sec. 21.

On request by the german egyptologist Ludwich Borchardt, J.H. Cole repeated the measure-
ments of the sidelenghts in 1925 and achieved the average 9069,4" or 230.364 m. The big-
gest difference was 20 cm between north- and southside. The paper is online here.

But in 1979 the sidelenghts were re-measured by Josef Dorner who achieved measures more
similar to Petrie's, and the average 230.360 m. Biggest deviation was 4.4 cm between the north-
and southside.

Measurements compared

Dorner has perhaps shown a small error in the measurements of the north- and southside by Cole.
Differences in baselenghts - measured by Petrie, Cole and Dorner - are very small. The strenght
of Petrie's measurements is that his exterior measurements of the pyramid "easily" can be con-
nected to internal measurements, making consistency, and therefore adopted at this webside.

It is widely accepted that the pyramid builders planned the baselenghts as 440 cubit. Then a
cubit must be close to 0.5235 meter (230.35 m / 440). This presumption is supported by the -
yet slighty different - lenght of the cubit used in the layout of the floor in the Queen's- and
the King's Chamber and elsewhere. More in Petrie, "Values of the Cubit and Digit", Ch. 20.

Sideangle 51° 52' or 51° 50' 40"

51° 52 - W.M. Flinders Petrie, 1883
51° 52 - I.E.S. Edwards, 1993
51° 50' 40" - Mark Lehner, 1997
51° 50' 34" - seked of 14 digits vertical and 11 horizontal

Petrie measured the layers or courses, block by block, of the stripped coreblocks. Northside
alone was 51° 50' 40''. This is read as 51 degres, 50 minutes and 40 seconds. It is based on
division of the circle into 360 parts or angle-degres, and each degre divided into 60 parts (minu-
tes), and each minute furthermore in 60 parts (seconds). Apart from the struggle in converting
from non-decimal measures of lenghts into meters, we also have to suffer with a babylonian
legacy and burden of a non-decimal division of the circle.

Northside alone was 51° 50' 40". This angle is very often stated as a mean for all four surfaces.
For all four surfaces, the estimated average was 51° 52'. In decimal: 51 + 52/60 = 51.867°.
The "rate of slopeness" is 1.2738, i.e. the height (146.71 m) of the pyramid divided by ½ of sideline
(115.174 m). Then, the height of the Pyramid was 115.174 m × 1.2738 = 146.71 meters (Petrie:
"5776.0 ± 7.0 inches"). To compare, a staircase is often between 35 and 45°.

A rod of 1 cubit for measuring were divided into 28 digits. And a use of 28 digits vertical and 22
digits horizontal (or 14 and 11), when chopping the facadeblocks, would give the angle 51° 50'
34". In decimal 51.843°.

Was the baseline put to 440 cubits, this method would give the pyramid a height of 280 cubits,
as half baseline is 220 cubits and 220 × 14 / 11 = 280 cubits.

Rate of slopeness for 14 / 11 is 1.272727etc. Then, the height of the Pyramid is 146.59 m. Cal-
culation: 115.174 m × 1.272727 = 146.59 m. See eventually also the drawing under "Com-
pleted height".

Present height 137.38 m or 5408.6"

Wikipedia English June 2008: "138.8 m, 455.2 ft".

When Petrie measured the Pyramid in 1881-82, course 202 and 203 were present in the
NE-corner, but have since vanished. Height of course 203 was 138.48 m. [Petrie, Plate 8].

The height of course 201 - still present - was 137.38 m - a height still used today. In fact, it was
a mean of two measurements along the edge of the Pyramid from both the NE- and the SW-
corner to course 201. And 137.36 and 137.39 m respectively.

On the top of the pyramid is today seen a metal construction which shows the original height
of the pyramid, i.e. the position of the peak of the missing topstone or apex of the Pyramid.

Completed height 146.71 m or 146.59 m

- Herodotus in 5th century B.C: "8 plethres" for both height and baselenghts.
- Wikipedia English, June 2008: "146.6 meter, 480,9 ft.".

The completed height can only be estimated due to loss of 15-20 courses at the top.

Use of baselenghts 230.348 m and angle 51° 52', gets height 146.71 m (115.174 m × 1.2738).
Petrie: "5776.0 ± 7.0 inch" or 146.71 m ± 0.18 m. Between 146.53 and 146.89 m.

It is widely accepted that the pyramidbuilders used a rod of wood for measurements. And
with markings that divided the rod into 7 handwidths and each handwidth into 4 fingers - see
drawing. Numerous rods, divided in this manner, has been found in Egypt.

Was a seked of 7 hands (28 fingers) measured vertical and 5½ hands (22 fingers) horizontal
under construction of the sideangle, the height became 146.59 m (115.174 m × 14 /11)
Or calculated thus: 115.174 m × 1.272727 = 146.59 m.

Was the baselenght planned as 440 cubits, the height would be 280 cubits (220 cubits × 14 / 11).

Facadeblocks on northside near entrance

On the photo is seen some of the facadeblocks below the entrance of the Pyramid. They
were discovered by Vyse in 1837 and created a lot of attension, as the angle of each block
would be the same for all of the four surfaces of the Pyramid. The height of the casingblocks
on the photo is close to 1.48 meters [Petrie]. The big proportions of the blocks is a constant
source of wonder about the ancient workers ability to shape and move objects of extreem
weight. Photo taken 1906 by the Edgar Brothers. From Egyptarchive.co.uk.

Area of surfaces - base 53 060 sq.m. or 13.111 acres

Area of base:
- 53 060 sq.m. (230.348 m × 230.348 m).
- 5.3060 hectars (ha)
- 13.111 acres
Area of surface(s):
- 1 surface (side area) is 21 482 sq.m. Calculation: [230.348 m × 186.52 m] / 2.
- 4 surfaces 85 928 sq.m.
- 5 surfaces, all, 138 988 sq.m.

A stunt in figure acrobatics is to point out that the square of
the height of the Pyramid (146,59 m × 146.59 m) is almost
exactly the same as the area of one of the four surfaces, i.e.
21 489 and 21 482 respectively.

Volume 2.595 million cubic meters

Formula for the volume of a regular pyramid is base × height / 3. Volume for Khufu's Pyramid:
(230.348 m × 230.348 m × 146.71 m) / 3 = 2.595 million cubic meter. The base was not fully
leveled, so untouched rock may fill up a considerably part of the Pyramid's volume. Perhaps as
much as 30 % acc. to Zahi Hawass, and a substantial reduction in a still gigantic work.

It is sometimes stated that the impressive Pyramid of the Sun in Mexico has the biggest
volume of all pyramids, but the volume is exaggerated. The book Seventy Wonders of the
Ancient World
(1999) states that the sidelenght is "226 meters" and present height "65
meters" without the missing temple on the top. Then, the volume is around 1.3 million cubic
meters, when height is put to 75 meters as a favorable approximation.

Pyramid of the Sun and Khufu's Pyramid compared Pyramids compared

Weight about 6 million metric tons?

It is impossible to give a reliable weight of the manmade part of the Pyramid for a number
of reasons:

- The volume of upstanding and untouched rock inside the Pyramid is totally unknown and
could be considerably.

- Densities, determined for blocks actually used for the Pyramid, seems to be found nowhere.

- Natural-stone.com states that density for limestones can vary much, from less than 1 760
kilo per cubic meter to more than 2 560.

Some guidence from simetric.co.uk (kg/):
"Basalt, solid 3011". Used for pavestones, from Fayum.
"Granite, solid 2691". Used for walls, cielings and more, from Aswan.
"Limestone, solid 2611". For facade from Thura. For core and more from Giza Plateau.

Some guidence from Petrie who used the density 2.21. (Petrie, Ch. 22, note 6).
Facade- and coreblocks probably occupy at least 98 % of the Pyramid's volume. Then
a maximum - and likely much exaggerated - weight could be the total volume with a relative
density of the facade- and coreblocks, i.e. 2.595 million × 2.611 metric tons per
= 7.0 million metric tons.

If untouched rock occupies as much as 30 % of the volume acc. to Zahi Hawass, then the
manmade part of the Pyramid could have a 30 % lesser weight, i.e. 4.9 million tons and still
a staggering weight.

Another approximation is to use Petrie's round off figures:
2.3 million blocks x 2.5 tons per block = 5.75 million imperial tons or 5.84 metric tons, as
1 imperial ton equals 1 016 kilograms.

Cornerangle 42.01°

Calculation: 146.71 m / 162.88 m = 0.9007. And 1 / tg (cotangent) to 0.9007 is 42.01°.
A cornerangle of exact the round figure 42.00° is well inside the margin of uncertainty, but
there is no reason to believe this angle was intended, as the architects of the Pyramid did
not divide the circle in 360 parts.

Longest way to the topstone 219.21 m

From one of the four cornerblocks and along the edge to the peak of the topstone or
"longest way to the top". Calculation, assisted by the handy theorem of Pythagoras:

Cornerblocks and top of the Pyramid are missing. To climb the outside of the Pyramid is
no longer allowed. It was and is dangerous. When allowed, an advice was to climb along
the edges with a lesser slope (40,01°) than between the edges (51,87°). Many gorgeous
and lovely photos has been taken, depicting victorian and edwardian ladies and gentlemen,
assisted by local guides, crowling up and - along - the edges.

Shortest way to the topstone 186.52 m

From exactly between two corners on the pavement to the peak of the topstone. Calculation:

About use of π (Smyth)

A publisher, John Taylor (1781-1864), promoted in his book The Great Pyramid - Who built
it and why was it built?
(1859) the idea that a biblical tribe builded The Great Pyramid with
a Godgiven knowledge about and with the perpose to handover this knowledge to genera-
tions ahead in eternal stones. Taylor noticed that the perimeter of the pyramid divided with
double height of the pyramid would give a figure close to . Use of Petrie's measurements
(baselenghts 230.348 m and height 146.71 m), gives:

And is tempting close with 3.1415etc.

The perimeter of the pyramid could be measured, and then the height of the Pyramid could
be calculated as (921.392 m / 3.1415) / 2 = 146.65 meters. And certainly within the range
of probability given by Petrie in 1883, i.e. between 146.53 and 146.89 meters.

The astronomer of Scotland, Charles Piazzi Smyth (1819-1900), promoted with force and
endurence in books after book the idea of Taylor about as a fundamental part of the Pyra-
mid's proportions. Smyth calculated the tangent (still using Petrie's measurements) as
146.65 m / 115.175 = 1.2733etc.
Corresponding sideangle of : 51° 51' 14.3". In decimal 51.854°.

About the wrong and exaggerated height of 147.80 m, sometimes stated in factual texts. In
calculating the completed height of the Great Pyramid, Smyth assumed an average of the er-
roneous and too big baselenghts by the Expedition of Napoleon, Vyse, and others. A base-
lenght of "9.140" inches (761.67 ft or 232.16 m), and consequently, the height of the Great
Pyramid became too big. And can be calculated as [232.16 m × 1.2733] / 2 = 147.80 m.
And stated by Smyth in Pyramid Inches as 5813,01. In British inches 5813.01 × 1.001 =
5818.82 or 147.80 in French and atheistic meters, according to Smyth.