Let's See more On-Screen Info (what is missing):

When I am playing through Civ IV games, there are often times when I wish that the program displayed more information about various things. One thing that comes to mind is the amount of Culture it takes to make a city "Legendary." If this info was simply displayed on the Victory screen, it would be great. Please add other things you'd like to see in future patches/mods.

The amount of culture you need is located in the city screen. It is in the lower left corner. Not only does it tell you how much culture you currently have, it tells you how much you're gaining every turn. The cultural boundries increase every time the bar fills up. You need three cities to reach 50,000 in order to win a cultural victory. After a city has reached 50,000, the culture keeps adding up, but the bar doesn't empty to re-fill. That is how I found out how much is needed to reach Legendary status.

It's not 50k culture for every speed, map size, etc.

But the space GeorgeOP mentions shows the correct value always.