Fortunately, most clogs in bathtub drains are caused by buildup of oily hair and scummy soap, and such clogs can frequently be cleared by the homeowner or do-it-yourselfer.
For the typical case of a clogged bathtub drain which has been building up over time, resulting in slower and slower draining, your first and most likely option for success is to try and remove the built up material from the pipe. Wearing rubber gloves remove any trap or strain restricting access to the drain. If you can see the blockage, try and remove it with your fingers, needle-nose pliers, or a coat hanger bent into a small hook on the end.
Plungers work by forming a seal so they can apply pressure and suction to push and pull on a clog until it breaks up enough for removal or flows down the pipe. If the plunger can't form a proper seal, it will not be able to do much to break up the blockage. This is why for a plunger to work on a bathtub drain you must first block up any secondary overflow drain. If you can't see the clog, nor reach the accumulated gunk with a bent wire, then it is time to try the plunger. It is not advised to use a plunger if you suspect something substantial or solid is causing the block--trying to plunge a shampoo cap or part from a child’s toy could just make the situation worse.
When removing this cover, cover the main tub drain with a towel. The shield is usually held in place with one or more screws, and you do not want to drop a screw down your drain! Also cover the main drain when you have finished clearing the clog and are putting the shield back into place. You will drop a screw! Many bathtub overflow drains are protected by a shielding plate with the lever controlling the stopper in the tub. It may be possible for you to form a seal without removing this fixture, but it is usually not a tight enough seal for a plunger to work.
Once any covering plate has been removed, stuff a wet rag or towel into the overflow drain to seal it up for using the plunger. Failure to block up the overflow will at the very least result in the plunger being ineffective, and at worst could shoot water or other liquid back at the person wielding the plunger, so make every effort to securely seal the overflow drain without letting anything fall into it. You may need a third hand, perhaps a helpful child, to hold this seal in place while you work the plunger.
Place the plunger opening over the bathtub drain. Remember that your goal is to break up the clog, not to try and push it "through". Plungers work better moving water than moving air, so if you are clearing a slow drain, add water until there is enough standing for the plunger to swish it back and forth in the pipe. Maintaining a tight seal around the drain, make several up and down strokes with the plunger. Afterwards, gently remove the plunger, taking care to avoid splashes as the seal is broken. If some of the blocking material washes up, it is best to remove it with gloved hands to be thrown away, as opposed to trying to wash it back down the drain. Large or resistant clogs may require several attempts, just keep in mind you want to bust the blocking material apart, not compact it tighter.
In the unlikely event that you can neither reach the clog with a wire, nor break it up with a plunger, you should carefully consider calling a professional. It is probable the clog is caused by something substantial requiring extraction and the plumbing could be difficult to reach as well as being substantially rusted or corroded, and there is not much more a homeowner can try without specialized equipment or risk to property. A professional would have the tools and expertise to solve this problem quickly and correctly.
However, if you have easy access to the drain pipes, own a handheld drain auger, more powerful plumber's snake, or a wet/dry shop vacuum, then you do still have options.
In the case of reachable plumbing, often the P-Trap (the tub version of a sink's U-Trap) can be removed with little effort, providing access to pipes you can clean out with your bent coat hanger and needle-nose pliers.
With your "snake"--or drain auger--first bore out the short length of pipe between the main tub drain and where it joins the down-pipe. To reach the other areas when clearing a bathtub drain, feed the cable in through the exposed overflow drain, which will have fewer, more gentle bends along the way than the tub's bottom drain. Only use an auger on a tub drain as a last resort, and only then if you are sure the stoppage is not between the lower drain and the main pipe where a cable will reach it. The heavy metal tips on most augers will scratch chrome, porcelain, or plastic tub surfaces, so exercise caution not to damage fixtures when using these tools.
Once you've cleared your bathtub drain of the primary blockage, run the hottest water possible through the drain for several minutes, rinsing away anything still clinging to the pipe walls.
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