How many elevators are there in a building?

Is the building a residential type or commercial type such as office spaces? à Office space

Is there any constraint on the number of people an elevator can carry at a time? à Assuming it can accommodate 20 passengers at a time

May I know the number of floors in the building? à assuming 10 floors

No. of elevators = No. of people that can be transported by 1 elevator in a certain time frame (A) / No. of people to be transported in that time frame (B)

Let’s start with the estimation of (A) in the above equation:

Assuming that each floor height is approximately 10 feet

Maximum distance to be traversed by an elevator one-way = 10*10 = 100 feet

1 foot = 0.3m è 100 feet = 100*0.3 = 30m

Speed of an elevator = 0.5m/sec and let’s assume the elevator waits for 10 seconds at each floor for people to climb in and out of the elevator.

Total time taken by the elevator to go up from the ground floor to the 10th floor = Total distance to be travelled/Speed of elevator + Wait time at each floor * No. of floors

= 30m/0.5m/sec + 10sec*10 = 300/5 + 100 = 60 + 100 = 160 sec = 160/60 = 2.66 minutes or 2.5 minutes

Time taken by the elevator to go up and come down = 2.5*2 = 5minutes (Assuming worst case scenario of elevator stopping at every floor while going up and coming down)

So, since we assumed elevator capacity of 20 people, 1 elevator can transport 20 people within 5 minutes and return to the ground floor.

Now, lets estimate (B) in the above equation:

From my previous workplace, I am assuming that each floor can accommodate around 300 employees

Maximum total employees on a workday = 300 * 10 = 3000.

Since we are experiencing a hybrid work environment, I am assuming on a single workday, approximately 70% of the folks would be available in office.

So, number of employees coming to office on a single workday = 70% of 3000 = 0.7*3000 = 7*300 = 2100.

Most of the employees come to office in a time-window of 9am-11am.

 Lets assume there is uniform distribution of employees coming in the 2 hours’ time window from 9am-11am

Employees coming in within 2 hours or 120 minutes = 2100

Employees coming in within 5 minutes = 2100 * 5/120 = 1050/12 = 350/4 = 87.5 ~ 90

So, every 5 minutes, 90 people are coming into office.

As estimated above, it takes 5 minutes to transport 20 people using 1 elevator.

To transport 90 people, number of elevators required = 90/20 = 4.5 ~ 4 or 5 (using the main equation).

Therefore, in an office building of 10 floors (300 per floor seating capacity) with elevator capacity of 20 people, 4 or 5 such elevators are required.