Counting the work

Big numbers become manageable when you cut them into small ones. Let us turn '2.3 million blocks' into a daily schedule, the way a project manager would.

Blocks per day. Suppose the pyramid was finished in 20 years, which is close to the length of Khufu's reign.

• Days: 20 × 365 = 7,300
• Blocks per day: 2,300,000 ÷ 7,300 ≈ 315
• If the crews worked 10 hours a day: 315 ÷ 10 ≈ 31 blocks per hour, that is one block about every 2 minutes.

Now change the assumptions. If crews rested on 65 days of each year, working about 300 days, the rate rises to about 380 blocks a day. If the job took half as long (10 years), the rate doubles to about 630 a day. A big number is only as solid as its assumptions, which is why historians quote a range.

Most of the pyramid is low down. A pyramid is wide at the bottom and narrow at the top. The part above a fraction h/H of the height is a smaller pyramid, with volume (1 − h/H)³ of the whole. For the part above half height, that is (½)³ = ⅛, only 12.5 percent of the volume. So 87.5 percent of the blocks sit in the lower half. The average block was lifted only about a quarter of the height, around 37 m, and the last few levels needed very few blocks.

How much lifting energy? Use the model E = m g h with the average lift of 37 m. One 2.5 t block: 2,500 × 9.81 × 37 ≈ 0.9 MJ. For all 2.3 million blocks: about 2 × 10¹² J. Suppose a person can put out about 75 W of useful work for 8 hours (an assumption), which is 75 × 8 × 3,600 ≈ 2.2 MJ a day. Then the lifting itself takes about 960,000 person-days, which is only about 130 people working full time for 20 years. The lifting is not the hard part. The hard part is everything else.

Logistics is the real challenge. Thousands of people need food, water, tools, rope, copper chisels, sledges, boats and housing, all delivered on time. Stone must be quarried, dressed, hauled to the river, floated, unloaded and dragged to the site, and every one of those steps must keep pace. If the quarry makes 315 blocks a day but the haulers move only 200, a pile grows at the quarry and the builders stand idle. Building the pyramid was less about strength than about planning, supply chains and managing people.