If a firearm has a calibre over 20mm it isn't officially designated as
a firearm, what is it designated as?

Hello goldenbowls,

Redhoss's comment appears to be correct.  I have seen several sources
define a cannon as a gun with a caliber 20mm or larger.  For example,
see:

- "cannon (modern) a large-calibre fast-firing automatic weapon,
generally taken to be between 20mm and around 57mm calibre"

"Gun and Ammunition Glossary" ("Rapid Fire: The Development of
Automatic Cannon, Heavy Machine Guns and their Ammunition for Armies,
Navies and Air Forces"), by Anthony G Williams
http://www.quarry.nildram.co.uk/Glossary.html

- "cannon somewhat arbitrary, guns 20mm and larger firing shells
containing a small explosive charge. ..."

"World War II Glossary, Terms, Definitions"
Cannon, Machine Guns, and Ammunition
http://www.ww2guide.com/glossary.shtml

- "Other large caliber guns (20mm and up) were sometimes called 'cannon'."

"Cannon" [final paragraph] 
Wikipedia
http://en2.wikipedia.org/wiki/Cannon

Some references to 20mm and even higher weapons use the term "gun". 
So, if you want to talk about a particular weapon, you might want to
do some research to determine whether "gun" or "cannon" (or even some
other term) is more commonly used in that context.  (Also, depending
on your prior knowlege of the subject, you might want to search for
definitions of "caliber" or "calibre", in order to determine the usage
of that term in a particular context.)
 
- justaskscott


Search terms used, in various combinations, on Google:

cannon
cannons
firearm
firearms
20mm
"20 mm"
glossary
calibre
caliber

Added confirmation to what I thought

Cannon ??

The "official" definition of firearm is in the National Firearms Act,
US Code Title 26, Chapter 53, Section 5845.

The National Firearms Act
http://www.atf.gov/pub/fire-explo_pub/nfireact.pdf

§ 5845. Definitions
"For the purpose of this chapter -(
a) Firearm. - The term "firearm" means (1) a shotgun having a barrel
or barrels of less than 18 inches in length; (2) a weapon made from a
shotgun if such weapon as modified has an overall length of less than
26 inches or a barrel or barrels of less than 18 inches in length; (3)
a rifle having a barrel or barrels of less than 16 inches in length;
(4) a weapon made from a rifle if such weapon as modified has an
overall length of less than 26 inches or a barrel or barrels of less
than 16 inches in length; (5) any other weapon, as defined in
subsection (e); (6) a machinegun; (7) any silencer (as defined in
section 921 of title 18, United States Code); and (8) a destructive
device. The term "firearm" shall not include an antique firearm or any
device (other than a machinegun or destructive device) which, although
designed as a weapon, the Secretary finds by reason of the date of its
manufacture, value, design, and other characteristics is primarily a
collector's item and is not likely to be used as a weapon."


Note that caliber isn't relevant to the definition, which can include
any "destructive device."

hlabadie-ga

information on how to make a silencer for a .22rimfire rifle