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The Vampire State Building is the tallest building in New New York City. It has 240 floors plus a clock on the top.
In 3013, Fry rented the roof garden on top of the building, because he wanted the moment in which Leela would agree to marry him to be special. He asked her to be there at six thirty. However, as his watch was fast, he thought that she was not coming, so he jumped off. In actuality, though, she was on time, having arrived five minutes earlier. The two returned there many years later, after Fry accidentally froze the universe, and drank the champagne that a janitor — János — had poured when Fry rented the garden. They were then joined by the professor.
The height of the building isn't mentioned in the series, however, it can be estimated. Comparing the building to existing skyscrapers we could assume each floor takes on average 10-11ft which would mean the entire building measured about 2640ft, not including the top. Including the top it would likely be comparable to the currently tallest building, the Burj Khalifa measuring 2717ft.
In the Episode 'Meanwhile' Fry jumps of the roof of the Vampire State Building. In this scene the height of the building becomes somewhat unclear. While falling Fry realizes he can use the time button to transport him back 10 seconds in the past, which he hopes will save him. We see him activating the time button for the first time when he is about 15ft above the pavement. He is transported 10 seconds into the past and appears just beneath one of the statutes below the top. This means that in about 10 seconds he would fall from the top to the bottom of the tower. When we calculate the speed of a free-fall on earth this means the tower is about 1700-1800ft high from the bottom to the platform. Since air resistance and terminal velocity was ignored the fall would actually be even shorter. In this case the tallest building in New New York would be about the same hight as the current tallest building in Old New York, the 'One World Trade Center' measuring 1776ft. However when comparing the number of floors in both buildings ( 240 to 104) it seems unrealistic that both buildings would be equally tall. Meaning that either vampires are shorter than present day humans or that the time button isn't that precise and sends Fry more than 10 seconds back in time. Alternatively it could mean nothing because Futurama is a cartoon and doesn't have to comply with real world physics and anyone who thinks it does is a moron.
In the episode Fry jumps at 9.08min and activates the button at 9.38min. It is hard to compare the time in the episodes with real time but in this scene we could assume that both are equal. This means Fry would be falling for about 25 seconds after he hit the statue. When factoring in terminal velocity and air resistance this would make the height of the Vampire State Building a lot more reasonable compared whit its' number of floors.