Bucky Isotope recently made mention of building the US-Mexico border wall entirely out of LEGO, following it with an inquiry on how much such a wall would cost. Twitter, even with the newly increased comment size, still did not provide ample room for the calculation with sources. This short piece will serve that purpose.
We will assume that the wall will be comprised of 2x4 LEGO brand building blocks for the sake of simplicity. It is possible that a more cost effective wall be made if a different piece is chosen as the basis, but it will suffice for our purposes.Credit: Cailliau.org
A 2x4 LEGO brand building block has dimensions 16mm by 32mm by 9.6mm.
If we simplify the surrounding border (heh) and remove the cap insets, shifting the volume instead to the perimeter by increasing the thickness to 1mm from 0.8mm, we can sum the four walls and 'ceiling' thusly:
Left: 15.8mm * 9.6mm * 1mm = 151.68mm^3
Right: Matches left.
Front: (31.8mm - 2mm) * 9.6mm * 1mm = 286.08mm^3 // We subtract 2mm for the thickness of the left and right walls.
Back: Matches front.
Top: (31.8mm - 2mm) * (15.8mm - 2mm) * 1mm. = 411.24mm^3 // Subtracting for the front, back, and side walls.
Total volume: 849mm^3 = 0.849cm^3.
At the time of writing, LEGO blocks are manufactured from acrylonitrile butadiene styrene (ABS), having a density of 1.05g/cc. A 2x4 LEGO brand building block then weighs approximately 0.89145g, giving us 1121 blocks per kg.
We can convert an average eBay cost of approximately $50/lb to $110.23/kg, or approximately $0.0893 per block.
The US-Mexico border is 3,145km long from the Gulf of Mexico to the Pacific ocean. Assuming blocks were stacked using the long side, it would take approximately 98,900,000 blocks for a grand total of $8,831,770.
The wall would stretch an impressive 9.6mm into the air and would weigh 88.16 metric tons.
If a taller or wider wall is required for some reason, one can calculate this by multiplying for every additional ~10mm of height desired and again for every 16mm of width desired. For example, doubling our wall from 9.6mm to 19.2mm would double the cost to $17,663,540. Doubling the width to 31.6mm would double the cost again to $35,327,080.
The average adult male from Mexico is 172 cm. To construct a wall with this height at a thickness of 15.8mm would cost approximately $1,582,358,791. It would require a human to be moving at least several centimeters per hour to breach.