Focusing solely on the question of focal length: a football field is about 160 feet wide.

* Simply assuming you're on the edge of the field and the graduate is straight across on the other side, assuming you're using a full frame camera you should be able to get a fairly tight shot of the individual with a 2700 mm lens (on a 1.5x crop camera you would only need about an 1800 mm lens).

* Unfortunately, you'll likely be in the stands and likely not able to get that close, so lets say you're another 50 feet away for a total of 210 feet from the subject, if the graduate is directly in front of you. You'll need a lens of roughly 3500mm on a full frame camera to get the same fairly tight shot. On a 1.5x crop camera you'll only need about 2400 mm.

* Both of those are likely ideal scenarios: with many graduates and families around you likely will be farther away and see many spots you wish you could get to for a photo. Let's round that distance up to 300 ft -- full frame: 5100 mm; crop sensor: 3400 mm.

Canon did make a [5200 mm lens](http://www.geek.com/news/canons-5200mm-prime-lens-is-super-rare-and-quite-massive-1534367/), but it's minimum focus distance is about 400 feet, so that won't work for you. More readily available is [Canon's 1200mm](http://www.bhphotovideo.com/c/find/newsLetter/Mother-of-All-L-Lenses.jsp). Nikon made a [1200-1700mm zoom lens](http://nikon.com/about/feelnikon/recollections/r16_e/index.htm) if you prefer zooms, and also made a [2000mm lens](http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/reflex/2000mm.htm). You may be able to carry some of these by yourself, but probably not when you include the required support equipment. And I'm ignoring costs completely!

Thinking more practically, a 300 or 400mm lens will let you get some nice group shots of the many graduates in the field from those distances. Focus on getting a shot of the graduate with diploma after the ceremony where you can pick a location, control the lighting, and prod them for a happy smile.