You shouldn't need a wrench to remove a showerhead because most are designed to be hand-tightened, and what you can tighten by hand you can usually loosen by hand. It's always possible someone stronger than you installed the showerhead, and in that case, you may need a little help.
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While not technically a wrench, adjustable slip-lock pliers will do the job, but their sharp grippers can easily damage the finish of the showerhead. You may want to look for alternatives, especially if the showerhead is stuck by rust or mineral deposits.
Augment Your Hand Power
The removal method recommended by showerhead manufacturers such as Waterpik is to grasp the showerhead with one or both hands and turn it counterclockwise. Use as much force as necessary, and even if the showerhead doesn't turn, the shower arm may unscrew from the fitting behind the wall. This is fine; it won't cause a leak and it allows you to take the showerhead and shower arm into your workshop so you can separate them.
If your hands keep slipping on the smooth showerhead finish, wrap a towel around the showerhead and try again. If that doesn't give you the traction you need, put on a pair of rubber gloves. In the end, there's a 99 percent chance of success using these simple methods.
Use a Strap Wrench
When plumbers need a wrench that can turn a pipe without damaging the metal, they turn to a strap wrench which, just as it sounds, is a lockable strap attached to a handle. Showerhead dealers, such as Shower Maestro, agree this is a good tool for this particular job. You don't need to break the bank by buying the most expensive one because a basic, inexpensive one will do the job.
Wrap the strap around the showerhead and tighten it by pulling it through the ratcheting lock. Some strap wrenches have rubber straps, but if yours doesn't, it could slip. To prevent this, wrap a rubber glove around the showerhead before attaching the strap. Once the wrench is secure, put as much force as needed on the handle to turn the head counterclockwise. This method should work even if the showerhead is badly stuck.
Dissolving Rust and Scale
If you can't turn your showerhead by hand, and you don't have time to get a strap wrench, you can usually unstick the showerhead by dissolving the rust or scale binding it. Rust and scale aren't the same thing, and you need different chemicals to dissolve them, but neither is difficult to get or expensive.
Start by spraying the showerhead connection with WD-40 or a similar spray lubricant. Give it 10 minutes to work, then try unscrewing the showerhead. No luck? Spray some more and try again, but if it doesn't work on the second try, it's time to go after the scale that a lubricant can't dissolve.
Fill a plastic sandwich bag with white vinegar, wrap the bag around the showerhead so that it's completely immersed, especially the connector, and secure the bag to the shower arm with rubber bands. Wait about 2 hours, then remove the bag, and you should be able to turn the showerhead by hand.