Dimensions of the Cheops-pyramid (Khufu's pyramid)
Numbers and figures of the Cheops (Khufu) pyramid:
The pyramid of Khufu - Output / performance - Building material - Dimensions of the pyramid - Dimensions in Royal Cubits - Sources
Cheops-pyramid (pyramid of Khufu)
Of the the famous Seven Wonders of the Ancient World the Great Pyramid of Khufu (Cheops) at Giza is the only one still standing. Even for modern men it is amazing how this man-made structure lasted so long.
The Giza pyramids must have made an incredible visual impact - at the edge of the desert three abstract geometrical symbols were rising, huge luminous white triangles reflecting the blinding light of the sun!
The pyramids on the Giza plateau are with 146.59m (Khufu / Cheops) and 143.87m (Khafre / Chefren) respectively the largest, however there are over 30 major pyramids and a myriad of smaller pyramids in Egypt.
Cheops-Pyramid
1. Entrance 2. Entrance cut by grave robbers 3. Subterranean chamber 4. Grand Gallery 5. King's chamber, relieving chambers, granite portcullis slabs 6. Queen's chamber 7. Shaft 8. Limestone plugging the air shaft A= "Air shafts"
Output / performance
Detailed calculations how many workers were necessary to build the pyramid
Overview pyramid building
Builder
------------------- |
|
Khufu (Chuefui-Chnum or Khnum-Khuf, Cheops in Greek) during the 4th dynasty of the old kingdom |
| Time to build |
|
Probably max. 23 years (Khufu reigned from 2551 to 2528 before Christ *). Herodotus writes about 10 years of preparation and 20 years of building (details of the text) |
| Per day |
|
With 2'500'000 stones 342 stones have to be moved daily (working during 365 days a year) or 431 stones daily (working during 290 days a year). |
|
Per minute
|
|
10-hour day: every 2 minutes a stone (34 to 43 per hour)
8-hour day: nearly a stone every minute (42 to 53 stones per hour)
|
| Rule of thumb |
|
| While construction the pyramid the rate of delivery was 1 stone weighting 2.5 tons every minute. |
For our calculations we assume 500 stones a day. This is a rough estimate, assuming a 8-hour day, during 290 days a year, with 20 years to build the pyramid. Also assuming, that more time had to be used for the huge granite blocks for the King's chamber and for the more difficult upper part of the pyramid, where work went slower than in the lower parts. There probably were also other factors delaying the building of the pyramid such as the weather or a temporary shortage of certain building materials.
|
Building materials for the Cheops-pyramid
The Khufu-pyramid (Cheops) probably originally had 210 stone layers. At 50m height already 82% of the entire pyramid was built [3].
Quarrying stones for the pyramid
Shipping the stone blocks down the Nile to Giza
Transporting the stone blocks using a sledge on tracks
Löhner's rope roll
Stone blocks
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|
2'300'000 stones |
| Casing blocks |
|
115'000 to 200'000 stones or 67'390m³ [1] |
| Total blocks |
|
2'500'000 stones |
| Stone layers |
|
Originally probably 210 stone layers, now only 201 layers [2] |
| Stone size |
|
The stone blocks usually are larger in the lower layers (1.5m = 3 cubit) and smaller in the upper layers. Most are between 1.5 and 2 cubit large (average of 127 x 127 x 71cm). 1 cubit = 0.524m - Details |
| Weight of the stone blocks |
|
With an average density of 2,6 - 2,9 t/m³ the large limestone blocks weighted 6.5 - 10 tons and the smaller ones about 1.3 tons. For all calculations on this website an average weight of 2.5 tons was used. |
| Special blocks |
|
For the King's chamber granite blocks weighting 40 to 50 tons were used |
| Total weight |
|
6'500'000 tons (average weight of a block was about 2.5 tons) |
| Pyramidion |
|
The final stone on the top was a large block in the shape of a pyramid. It was perhaps around 1.5m by 1.5m wide and 1.3m high (about 3 cubits). It was made from white Tura limestone (Turah), granite or perhaps diorite and perhaps gold plated. More information |
| Building materials |
|
Pyramid: Nummulite limestone from quarries about 200-400m south of the pyramid were used for the core stones.
Casing: light white limestone, so called Tura-limestone from quarries from the eastern shores of the Nile
King's chamber: Rose granite from Aswan 900km away
Further materials: Graywacke from the Wadi Hammamat (Eastern desert), basalt from the northern Faiyum
Map of quarries in Egypt
|
Dimensions of the pyramid of Khufu
Length (a)
------------------- |
|
The average length of the edge is ~ 230.360m (230,12m = 440 cubits). Northern edge 230.328m - eastern edge 230.369m - southern edge 230.372m - western edge 230.372m. Largest difference is only 4.4cm. [3] |
| Height (h) |
|
Originally 146.59m high (= 280 cubits), the pyramid is now only 138.75m high [7] |
| Diagonal (d) |
|
325.77m |
| Ridge (g) |
|
219m |
| Height of the lateral surface |
|
186.42m |
| Pyramid angle α |
|
51° 50' 40' = inclination of the lateral surface (= 52° rounded off) [3] which corresponds to a seked of 5½ palms |
| Pyramid angle β |
|
58.3° = the two angles of the triangular lateral surface (62° = angle of the apex or tip of the pyramid) - nearly forming an equilateral triangle! |
| Pyramid angle γ |
|
41.9° = angle of the ridge |
| Corner angle |
|
Right angle base with angles from 89° 59' to 90° |
| Base area |
|
53'065.73m² |
| Superficies surface |
|
85'890.69m² |
| Pyramid volume |
|
2'592'968.43m³ including the rock core. This would be a cube with a length of 137.38m. Probable volume of stones used: 2'583'283m³ [1] or 2'326'501m³ [2]. |
| Alignment |
|
Exactly to the north (deviation only 2' 28') |
| Latitude and longitude |
|
N 29° 58’ 44.3830” latitude and E 31° 07’ 57.0194” longitude [5] |
| Altitude |
|
The base of the pyramid of Khufu lies about 60m above sea level, so the tip of the pyramid used to be on 206m above sea level [6]. |
Alignment of the pyramids and controlling the shape of the pyramid (north-south alignment etc.)
Dimensions of the pyramid of Khufu in Egyptian Royal Cubits
 |
Length (a) |
|
440 Royal Cubits |
| Height (h) |
|
280 Royal Cubits |
| Height of the lateral surface (c) |
|
356 Royal Cubits (356.09) |
| Diagonal (d) |
|
622.25 Royal Cubits |
| Ridge (g) |
|
418.56 Royal Cubits |
| Pyramid angle α |
|
51.843° |
| Pyramid angle β |
|
58.3° |
| Pyramid angle γ |
|
41.9° |
| Corner angle |
|
90° |
It is suggested, that the Egyptians used a right angled triangle to determinate the angle of inclination of the pyramid, using the numbers a=11 and b=14 with c=17.8 (or a=22 - b=28 - c= 35.6). This determines a so called seked of 5½ palms.
Alignment of the pyramids and controlling the shape of the pyramid (seked)
Sources
[1] M. Lehner The Complete Pyramids of Egypt
[2] G. Goyon Die Cheops-Pyramide
[3] R. Stadelmann Die grossen Pyramiden von Giza
[4] F. Abitz Der Bau der grossen Pyramide mit einem Schrägaufzug
[5] GPS-coordinates of a brass disk on top of the pyramid of Khufu, Giza Plateau Mapping Project (GPMP)
[6] Maps of the Giza Plateau Mapping Project show the altitude as 60m
[7] D. Arnold Building in Egypt
* Dates according to conventional Egyptian chronology are used in this website. These are based on several list of the dynasties of pharaohs, for example the Aegyptiaca of Manetho of Sebennytos.
https://www.cheops-pyramide.ch/khufu-pyramid/khufu-numbers.html 
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