How to extract a broken off 1/2 inch threaded galvanized pipe

If you buy the pipe at Home Depot, they custom cut it (and thread it) for free. You have to buy the pipe, and there is a fairly flexible policy that they will make up to three cuts per 10 foot length, but if you catch them an hour before closing or when it is not otherwise busy, they are very accommodating.

I use to run a pipe threader at Home Depot, and my cuts always fit just like the pre-threaded pipe. Their machine could have been out of adjustment. If the threads don't look the same as a pre-threaded pipe, and they don't fit the same, something is wrong.

For what you're doing, 1/4" of pipe thread might not provide the strength you need even though it doesn't have to be water tight. Take it back and show them the problem.