The Great Pyramid of Khufu was laid out 440 royal cubits square and 280 cubits high, a seked of exactly 5½ palms and a slope of about 51°50′.
½ × 440 ÷ 280 × 7 = 5½ palms → arctan(7 ⁄ 5.5) ≈ 51.84°
Rules · Geometry · Proportion · Modules
The seked of a pyramid
Specify the slope of a pyramid face by its seked: the number of palms (and fingers) by which the face runs inward for every cubit of rise. The height follows from half the base divided by the seked, times seven.
seked = 7 × (½ base ⁄ height) palms · angle = arctan(7 ⁄ seked)
Egyptian scribes had no angles. They gave a slope as a ratio of run to rise expressed in their building units: the royal cubit of seven palms, each of four fingers. A seked of 5½ palms means that the face moves 5½ palms inward for each cubit it climbs. In practice a mason could set this out with a square, a plumb-line and a measuring rod, block by block.
The Rhind Papyrus works five examples. In Problem 56 a pyramid with a base of 360 cubits and a height of 250 has a seked of 5 1⁄25 palms; in Problems 57–59 the seked is 5 palms 1 finger, which gives the slope of a 3 : 4 : 5 triangle, about 53°. Try the slider: the model recomputes height and angle from the seked.
Related rules
Lay out Egyptian buildings in royal cubits (≈ 52.4 cm) of seven palms of four fingers, so that every dimension and every slope can be stated in whole or simple fractional units.
1 royal cubit = 7 palms = 28 fingers ≈ 0.524 m
When a steep pyramid shows signs of distress, flatten the slope of the upper part: Sneferu’s pyramid at Dahshur rises at about 54° for its lower part and about 43° above.
lower seked 5 palms (≈ 54.5°) → upper ≈ 7½ palms (≈ 43°)
Cut a shaft with sixteen shallow flutes or facets, give it a square abacus and a low round base: the “proto-Doric” column of the Middle Kingdom rock tombs at Beni Hasan.
Cut the obelisk from a single block of granite, square in section, tapering to about two-thirds of its base width, capped by a pyramidion, and about ten times as tall as it is wide; set them in pairs before the pylon.
height ≈ 9–11 × base width
Find a granary’s capacity from its measures: multiply length, breadth and height in cubits (or, for a round bin, the square of eight-ninths of the diameter by the height), and add half as much again to turn cubic cubits into the grain measure, the khar.
1 cubic cubit = 1½ khar
Cite this page Chris Paton, “The seked of a pyramid”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/seked-slope. Text, drawings and models licensed under CC BY-NC 4.0.