Our glorious, dead-letter Constitution states that the "right of the people to keep and bear Arms, shall not be infringed." I know this will infuriate you statist heathens with an ax to grind, but 'not infringed' means if you're tall enough to put your money on the counter, you can have a gun.
Stick that in your pipe and smoke it you anti-gun anal buccaneers.
Aside from the absurd "tall enough to put your money on the counter" extrapolation, you still didn't answer the question about how you go from "arms" to "handgun." If you can interpret the word "arms" to mean extend to handguns why can't I also interpret universal healthcare from the right to life?
Oh--and just in the interest of full disclosure, I own a handgun.