Estimate Empire State Building Weight

Approach

This estimation question's strategy is straightforward: break down the question into its components, then sum the total. So, what is the Empire State Building is composed of? Here’s a short list:

• Brick and steel structure
• Walls
• Floors
• The top of the building
• Furniture

Let’s focus on the brick and steel structure, since it is the most significant contributor to the weight of the building.

Stone/Brick

The stone/brick in the building will generally be used for the exterior. Let’s calculate the exterior area of the building.

Let’s estimate the perimeter of a NYC block first. Blocks are not square, so start by estimating how much longer the blocks are than they are wide. Let’s start with an initial assumption that blocks are thrice as long as they are wide. Let’s estimate that the short side of the block is about 200 feet. How did we come up with this number? A human step is about 4 feet long, and it takes about 50 steps to traverse one block. Thus, our perimeter is 200 + 200 + 600 + 600 = 1600 feet.

Now that we’ve calculated the perimeter, we’ll need to estimate the height to calculate the total exterior surface of the Empire State Building. We know the Empire State Building is 100 floors tall, so we just need to estimate the height of a single floor and multiply by 100. We can base our estimate from human height; for instance, I’m 6 feet tall and it usually takes about two of me to reach the ceiling of a professional building like the Empire State. Thus, each floor is 6 feet * 2 = 12 feet tall. Then, our building height estimate is 1200 feet.

Let’s put these numbers together. Our 1600 feet perimeter building rises 1200 feet in the air, so the total exterior will be about 2 million square feet. That’s a lot of square feet!

Our last calculation for this section: how much does a square foot of stone/brick weigh? If you imagine carrying a square foot of brick, you could imagine it being heavy, but certainly light enough to be lifted. Therefore, let’s estimate that a square foot of stone/brick weighs about 50 pounds with all the required reinforcements.

Multiplying our 2 million square feet perimeter * 50 pounds per square foot = total weight of 100 million pounds.

Floors

We’ve forgotten a big piece: the floors themselves. We’ve only calculated the building exterior, but not the interior. Let’s assume the floors are composed of a similar weight per square foot ratio as the exterior walls. We have 100 floors with a total of 200 * 600 = 120,000 square feet per floor. 100 floors * 120,000 square feet * 50 pounds = 600 million pounds.

Interior Walls

The last major piece is the interior wall weight. First, let's estimate the size and number of walls in the building. Roughly, it's a reasonable assumption to state that there is half as much wall area in the building as floor area (we definitely know that wall area and floor area are correlated numbers). However, the internal walls weigh far less than the harder exterior and the floors of the building. Let’s estimate these interior walls as also weighing about half as much. So our equation for wall weight is 25 pounds * 100 floors * 60,000 square feet = 150 million pounds.

Final Estimate

Our final estimate? 150M + 600M + 100M = 850M pounds.

After all these considerations, there are still even more that are worth mentioning in your interview if you have time. Here are a couple:

• The top piece. The Empire State building has a large decorative top piece which adds to the weight. This one is hard to estimate, but you’ll need to guess about how tall and wide the piece is, and how much it might weigh.
• Elevators. The weight of an empty elevator isn't likely to significantly increase the overall total, but when considering there may be up to 100 elevators in the building, it might be worth a mention.
• The furniture. Regardless of calculating it, furniture is a good factor to mention to show that you’re thinking critically about what goes into a building’s weight. You can estimate the quantity of furniture and average furniture weight.