Noticed how sometimes you're offered a table in a restaurant, you sit, and then realize table wobbles once you touch it or put your hands on it? That's often a minor nuance that doesn't affect table main function but can be quite an annoyance.
Sometimes, when you receive your new dining set same happens to those dining chairs you just assembled. They wobble. While you can safely use them, it's quite an annoyance. You start to think chairs are faulty, defective or something is wrong with them, but in reality, it's never the case. It's just how you install them.
Fortunately, it's quite easy to fix. Tables in restaurants and chairs, either new or used do wobble for pretty much almost the same reasons: either legs connections become loose, or those legs connections are tightened incorrectly. Let's see what you can do in order to get rid of a problem. Make sure you have nothing wobbles as it's loose.
First thing to check - see if all legs / bolts / nuts are tight. This is the first thing you'd need to check when you have a wobbly leg situation. If everything is properly tightened, go to step 2.
Final assembly tightening should be done in 'standing' position
Most of dining chairs (bar stools, bar chairs, etc.) are designed in a way when base / legs are either pre-assembled or pre-done in parts (like 2 and 2 legs are pre-made in factory so they are connected to a single piece). In those cases, you'll never have any wobbly chair problem. However, at least 50% of all chairs are designed in a way that those can be really sensitive on how the chair is assembled.
Typically it happens when all 4 legs are independently connected and tightened.
Main trick here is to never tighten everything up right away, and first place a stool or chair to a vertical position. Just install every piece of hardware and tighten everything moderately. Do not tighten everything completely while chair is laying on a back! This a typical mistake people make, since obviously it's easier to assemble something like chair while chair ifself is enjoying it's time on a back.
You have to place the chair into position as it will stand when used. Vertically. Then you'd have to apply a little pressure on a seat, some chair can even be seated on (depends on a chair). Slightly play with a chair and let it 'settle' with applied weight. Only then you can carefully tighten all 4 legs up by using circled approach: if you name 4 legs by numbers, 1,2, 3 and 4, try to move in circles with your tightening, 1, 2, 3, 4, 1, 2, 3, 4 and so on.
Lightly sitting on a chair can be a best way to even up the chair before final tightening
This way you'll ensure the chair will be assembled as properly as it can be. Most of wobbly chair 'problems' will be gone with this step properly done.
Carpets and Area Rugs
While above method works to eliminate over 95% of wobbly chair problems, some chairs will be very sensitive anyway and will experience minor wobble no matter amount of adjusting you'll do.
Some things that have 4 legs are just designed this way and you'll have to apply a different approach if some minor wobble still bothers you.
Consider if you can use those products on area rug or carpet. Very sensitive chairs tend to be designed to be used with rugs or carpets. They will just be too sensitive for a bare floor.
Area rugs can be easiest and best solution for minor wobble
Besides area rugs give great extra decor, coziness and value to your place + eliminate a portion of sound reflections + noise.
Furniture Pads: buy Pre-Made or make Your Own
Practical and easy furniture pads can be a good advice any way
Final thing would be to get a furniture pads. You can easily buy these in any store like Home Depot or Walmart or just make them yourself. These can be very beneficial - you'll eliminate a chance to scratch a floor + will ensure more subtle legs action along with your hardwood floors or carpets. Furniture pads cost pennies but can be very beneficial for variety of reasons including wobbly chair fix.
You can also make these out of pretty much anything, but these pads typically cost that little it's easier just to buy them.
Pads are great and can be recommended regardless, however proper assembly should be done as #1 thing, since that is primary reason for extreme or unpleasant wobble.