I snapped a screw tap in the hole tonight while tapping a thread for a rail on a Remongton 870 Magnum Express shotgun.

The first one went smoothly, then on the second hole I found it wasn't deep enough and, since I had measured the drill bit and knew the hole was deep enough I decided to try to run the tap deeper...

On the way back out, even though I was very careful the tap broke.

It will move slightly back in and out, but there seems to be a burr stopping it from coming back out.

I thought of cutting it off flat and trying to drill it out but having already botched part of it and not having a dril press I decided to call it a night.

It there a trick to getting broken taps out of holes or should I just take it to a good smith to drill out?

Also the thread I cut was M3.5mm - will drilling it out mean I have to go to a bigger screw? I have some other (imperial) screws, I think they are 8/40th or something like that, around 4.10mm diamter that would do the job too.

I am in a bit of a jam here, any advice would be appreciated.
Thanks.

if you have access. to ..a broken tap extractor.
Try a local machine shop?
Personally I would reframe from trying to drill, the tap is very hard and will destroy drill bits.
You may be able to use a small punch with a very sharp point and tap lightly on alternating flutes of the tap and back it out.
I have had luck with a needle nose plires sharpened to a point inserted into yhe flutes and turn the tap out.
Dave

Express.

If you can work the broken remnants out by working back and forth with fine noed pliers then that will be a result.

I very much doubt you will be able to drill out the core as the tap will be of either a carbon steel or High speed steel and effectively too hard to touch with a drill. Maybe a toolmaker close by with access to a milling/ drilling machine could attempt to drill out with a carbide drill, but the shape of the tap would make this difficult as the drill tip would snag on the flutes of the tap and as carbide is hard, it is also very brittle, you could then end up with both a broken tap and parts of a carbide drill in the hole.

Possibly a better way is to find a toolmaker who has a spark erroder, this is a machine that cuts steels and carbides by electro discharge, I say toolmaker as few gunsmiths will have such a machine. Once the action is set up an electrode discharges high amperage current into the tap and slowly erodes away the steel, the process is not particularly quick and may even be costly, but it will remove the broken tap.

It may also be necessary to tap out the hole to the next size of thread, especially as damage has been done to the existing threads.

This has worked well for me in the past. The little dental burrs that your favorite mouth butcher thows away by the scores will slice right through a h.s. tap when used in a dremel or foredom high speed grinder. Use a small ball end burr and just slice the flutes off of the tap and it wll come right out. Keep it off the threads and you wont even have to retap.
Had to use one two weeks ago on a busted tap for a friend. Friend owes me big now.
okie

how deep into the hole? and a guess at how much of the tap is in it? I've used the dental burrs, like okie says, as well as extractors... and have "shattered" the tap, if there's not much, and gotten the pieces out...

call a local machine shop and ask if they can help you get it out

Find soneone with a milling mashine, install a coated 3mm carbide mill, alighn it excaktly over the center of the broken tap. Start the mill at 10.000rpm, and mill/drill the broken tap out.
One of those "throw away" short carbide mill cost in 3mm les than 12EURO or 15$m

I've tried different methods, some work well, others have a high pucker factor. Okie's method of using dental burrs is my new preferred method. I use the long slender diamond burrs. They are skinny enough to fit down the flute of even a #6. Slow, steady pressure does it. Too much pressure will break the burr. Fish it out, get another one. They're free. After you've gone from one side to the othe of the broken tap, wack it with a punch and the piece will fall through. It is a through hole, right? The only danger is a dinging the threads on the back side of the burr as you start out. It's only a small ding and does no harm to the finished thread.

I have several very small carbide endmills. They work very well.
Butch

Those cheapo chinese diamond burs that Harbor Freight sells work great at grinding out taps. With my binoc magnifiers on, and a Dremel tool, I even drilled out a 4-40 stub out of a Garand receiver. Skinny cone shapes work for me.