Extracting a broken screw can be a frustrating task. Extracting a small broken screw can be even more trying because there is less metal to latch onto, and its size makes it more difficult to use normal-size tools. When a screw is broken, it means its head has broken off. The best way to remove a broken screw largely depends on how much of the remaining shaft is accessible.
Grasp the shaft with vise grip pliers, and turn it counterclockwise. Try turning the shaft both ways. Sometimes the back-and-forth action helps break it loose.
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Apply a penetrating oil such as Liquid Wrench to the shaft of the screw. This is particularly effective if you do not have to remove the broken screw immediately. The oil works better the longer it is allowed to seep in. Remove the screw by turning it counterclockwise with vise grip pliers.
Heat the screw with a soldering iron or butane pencil torch. You can also heat a metal rod, and touch the screw with the rod. Make the screw as hot as possible without damaging the surrounding area. Allow the screw to cool to the point that you can touch it with a finger. Remove the screw with vise grip pliers.
Drill a small hole into the shaft of the screw. Tap a screw extractor into the shaft with a hammer. Attach a wrench to the screw extractor. Turn the wrench to remove the broken screw. If the screw still won't come out, hit the screw extractor with a sharp rap. This may also break the broken screw loose.
Completely drill through the screw. Drill again with a larger bit if practical. Drill until only small remnants of the screw remain. Remove remnants with a small, pointed object.