It is quite easy actually. If you want to know what size it would require just divide the focal length with the required f-stop and you'll see what size the front element diameter would be. So, for a 100-400mm f/1.2 the front element would be 33,3cm in diameter.
If you divide the focal length with the diameter of the front element you'll get the maximum f-stop for that lens.
i don´t quite get the math....
can you show how f1.2 gives 33,33 cm on a 100-400mm lens?
it´s more like 83mm for the 100mm end.
A 100-400mm f/1.2 lens (which will never exist) would need to have a 333.3 mm (13") front element - a practical impossibility. Your comment about needing an 83mm front element for the 100mm end isn't relevant - the front element can't change size so the optics must be sized for the long end. That's why the 100-400mm lens is a variable aperture zoom with an f/5.6 long end - if it was f/4.5 throught the zoom range, it would need an 89mm front element.
by the way:QuoteThe number for lens f/stop in photography (for example, f/8) is the ratio of lens focal length divided by the effective lens aperture. Aperture is not the obvious physical diameter, but instead is the apparent "working" diameter as seen through the magnification of the front lens element.
While the above is true, it actually depends on the design of the lens (Roger Cicala has an article on lens designs that's worth a read). With a telephoto design, the 'apparent working diameter' or 'virtual aperture' of the lens actually sits right at or just behind the front element.
Put another way, the front element generally needs to be at least as large as (focal length ÷ f/number), and with many lens designs the front element is significantly larger than that.