To ensure fence posts do not fall over easily, even in high winds, many fence installers set the bottom of the posts in concrete. While the concrete acts as an excellent anchor for the fence post, it presents a problem when the fence post breaks and you need to remove it from the ground. Usually the concrete is heavy enough you cannot simply lift the fence post out of the ground even after you dig around it. With the right tools, some time and muscles, you can remove the post.
Use a shovel to dig a hole around the broken fence post. Dig down until you find the bottom of the concrete attached to the bottom of the fence post.
Widen the hole so that there is a least 6 inches of space around the piece of concrete. You will need this space to remove the concrete.
Put on protective gloves and eyewear. Place the tip of a cold set chisel on the concrete and strike the other end of the chisel firmly with an engineer's hammer.
Continue striking the cold set chisel in the same spot until you crack the concrete. Move the cold set chisel to another section of the concrete and begin striking it with the engineer's hammer as before, repeating the process until most of the concrete has broken off the bottom of the fence post.
Lift the post out of the hole and remove the concrete chunks.