Pyramid of Khafre
01 · ContextKhafre's pyramid complex at Giza
Khafre's pyramid occupies the middle position among the three great royal pyramids at Giza. Its higher setting and the conspicuous band of casing remaining near the summit give it a commanding profile beside Khufu's larger pyramid. The apparent rivalry is therefore a lesson in landscape as much as in dimensions: elevation and preservation change what a visitor sees before any measurement begins.1
The monument belongs to a larger Fourth Dynasty funerary complex. The Egyptian Ministry's monument record identifies the pyramid, mortuary temple, causeway, valley temple and the Great Sphinx as connected elements of Khafre's setting. Its account also distinguishes the local limestone core, the upper Tura-limestone casing that remains visible, and the granite and alabaster finishes of the valley temple.1 The pyramid is best read within that built landscape, rather than as an isolated triangle.
02 · FabricConstruction materials and surviving casing
A clean diagram is useful, but it is not the monument. Richard Jones's construction study opens its Khafre chapter by warning that the pyramid is not a perfect structure: the core includes blocks of varying form and size, rubble occurs within it, and surviving casing thicknesses vary. His summary of the underlying archaeological discussion describes a slight twist in the plan rather than an ideally square platform.2
“The pyramid is not square as it twists slightly.”
That unevenness matters for proportional claims. A numerical profile compresses the monument into a base, a height and a square-pyramid assumption. It can show how a reported envelope behaves, but it cannot convert irregular core masonry, damaged casing or an inferred summit into a set of exact ancient instructions. The page therefore keeps the published model and the surviving fabric in separate rows.
| Quantity | Value | Basis | Limit |
|---|---|---|---|
| Base lengthPublished model | 215 m | Jones's construction-rate input | Used as a whole-number model input |
| Original heightPublished model | 143.5 m | Jones's construction-rate input | Lower than Khufu despite the higher ground |
| Face angleDerived | 53.162° | arctan(143.5 ÷ 107.5) | Depends on the two published inputs |
| Slant heightDerived | 179.30 m | Square-pyramid right triangle | Geometric result, not a separately measured edge |
03 · ProfilePublished dimensions and slope calculation
Jones gives Khafre a 215 m base, a height of 143.5 m and a face angle of 53.162 degrees in a construction-rate model. He also gives roughly 145 courses, using the resulting average only to calculate an overall building rate.2 That purpose is important. The figures are well suited to a transparent profile calculation, while the variable course heights described on the following page show why an average cannot stand in for every stage of construction.
For a square pyramid, the relevant right triangle runs from the centre of one side to the apex. Half of a 215 m base is 107.5 m. Combined with a 143.5 m rise, it produces a slant height of about 179.30 m and the stated 53.162-degree face angle. Expressed as a seked-style comparison, the run is 107.5 ÷ 143.5 = 0.7491 royal cubit for each cubit of rise. With seven palms to a royal cubit, that is about 5.24 palms.
| Step | Rise | Run | Result |
|---|---|---|---|
| Whole half-profile | 143.5 m | 107.5 m | 1.3349 rise : run |
| Seked-style expression | 1 royal cubit | 0.7491 cubit | 5.24 palms |
| Modern angle | 143.5 | 107.5 | 53.162° |
The last two rows translate the same slope into different languages. They do not establish an excavated cubit count, nor do they show that the published decimal inputs were ancient design values. They make the arithmetic inspectable and preserve the distinction between geometry and historical attribution.
04 · ProportionTesting the 3:4:5 proportion claim
An exact 3:4:5 profile with a 143.5 m rise requires a 107.625 m run and a 215.25 m base. The published construction model gives a 215 m base instead. Its half-profile is 107.5 by 143.5 by 179.30 m, which is close to, but does not equal, a 3:4:5 triangle.
There is a useful distinction here. A 3:4:5 profile can be constructed exactly from 107.625 m run, 143.5 m rise and 179.375 m slant, but that first number implies a 215.25 m base. Once that extra quarter metre enters the calculation, the result becomes a different model and needs its own documentary basis. Treating it as a measurement would conceal the choice that created the result.
05 · MeaningKhafre's place in the Giza complex
Khafre's pyramid makes scale visible at two levels. Its elevated platform and surviving cap of casing create a powerful visual relation with Khufu's pyramid. At ground level, the valley temple, causeway, mortuary temple and Sphinx give that profile a ritual and architectural setting. The combination is more revealing than a search for a single privileged ratio.
The Egyptian royal cubit dossier explains the measure used for comparative calculations across this site. For a nearby control, compare Khufu's Great Pyramid, whose documented reconstruction has a different slope, and then Menkaure's pyramid at a smaller scale. The seked guide and false precision set out the broader rules for reading those comparisons.
06 · SourcesSources
- Egyptian Ministry of Tourism and Antiquities, Pyramid Complex of Khafre (Khefren). Current monument record for the Giza setting, complex, core, casing and associated temples. Read the record.
- Richard H. Jones, The Use of Manpower in Pyramid Construction (2006), pp. 170-172, for the complex description, material variability and published 215 m base, 143.5 m height, 53.162-degree face angle and approximately 145-course construction model. Registered project source; page images read for this article.