The Great Pyramid of Giza was built circa 2600 BC and was the world’s tallest structure for nearly 4000 years. It consists of an estimated 2.3 million blocks with a weight on the order of 6-7 million tons. How many people did it take to construct the Great Pyramid? Vaclav Smil in Numbers Don’t Lie gives an interesting method of calculation:
The Great Pyramid’s potential energy (what is required to lift the mass above ground level) is about 2.4 trillion joules. Calculating this is fairly easy: it is simply the product of the acceleration due to gravity, the pyramid’s mass, and its center of mass (a quarter of its height)…I am assuming a mean of 2.6 tons per cubic meter and hence a total mass of about 6.75 million tons.
People are able to convert about 20 percent of food energy into useful work, and for hard-working men that amounts to about 440 kilojoules a day. Lifting the stones would thus require about 5.5 million labor days (2.4 trillion/44000), or about 275,000 days a year during [a] 20 year period, and about 900 people could deliver that by working 10 hours a day for 300 days a year. A similar number might be needed to emplace the stones in the rising structure and then smooth the cladding blocks…And in order to cut 2.6 million cubic meters of stone in 20 years, the project would have required about 1,500 quarrymen working 300 days per year and producing 0.25 cubic meters of stone per capita…the grand total would then be some 3,300 workers. Even if we were to double that in order to account for designers, organizers and overseers etc. etc….the total would be still fewer than 7,000 workers.
…During the time of the pyramid’s construction, the total population of Egypt was 1.5-1.6 million people, and hence the deployed force of less than 10,000 would not have amounted to any extraordinary imposition on the country’s economy.
I was surprised at the low number and pleased at the unusual method of calculation. Archeological evidence from the nearby worker’s village suggests 4,000-5,000 on site workers, not including the quarrymen, transporters and designers and support staff. Thus, Smil’s calculation looks very good.
What other unusual calculations do you know?
