I have a 19 inch tall american staffordshire terrier, how tall should
a fence be to ensure he cannot escape my yard?

Hello bbc1981~

Although your dog is small, you?ll want to consider it?s personality
before you decide how high its fence should be. If your dog isn?t a
?jumper,? the general recommendation is for a 3 ½ to 4 foot fence. (An
example of this recommendation: Friendly Fence, ?Dog Fence Kits,?
http://www.friendlyfence.com/ff/prod_fence_kits.asp )

However, if your dog likes to jump, or is apt to jump because it wants
out of the yard, a number of pet ownership sites recommend a 5 to 6
foot fence, even for a small dog. (For example, ?Fencing For Your
Dog,? Pet Place: ://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&c2coff=1&q=small+dog+fence+high&btnG=Search
)

Regards,
Kriswrite

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generally good answer, but the fact that this particular dog breed is
prone to jumping was not adressed until the comment afterward.

Kriswrite-ga has given you some excellent general advice, but I think
that one kennel's answer to your specific question can be found here:

"How high of a fence do I need? You need at least a six foot fence. Be
warned, however, that many APBTs can jump even a six-foot fence if
motivated. Six-foot privacy fences are a good idea because the dog
can't see all the temptations that pass by. However, observe your own
dog. Some dogs are jumpers, others are not. If you do have a dog that
is a jumper, consider combining an electric gate with a physical gate.
Or put a hot wire at the top of the gate."
Vegas Kennels: The American Pit Bull Terrier
http://www.vegaskennels.com/facts.html

My family had several Staffies growing up and they were *all* jumpers.
 I swear they had springs in their paws like Rod Stewart had
spring-loaded knees, before he developed geri-knees, of course.

A fence of 6 feet at the very *least*!  And if there's anything they
can climb on that's near the fence (like a dog house, trash can),
they'll just use it for their own private launching pad.

Cheers,
V