Will 12 inch subwoofer be enough for an 18x20 room (with 10 ft cielings)

Enough for what? It'll add bass for sure. But you'll end up overdriving it to get as much out of it to fill the room creating a hotspot leading to imbalanced sound. Best to use two, even if they're smaller. 

Using one subwoofer has always worked out fine for me!

FWIW, I have a large room with one sub. REL S3. It's fine but I find what I wrote above to hold true. I'm saving for another.

I have an SVS SB2000 (sealed box) that has a 12” driver and goes down to 19Hz within 3dB.  I have a similarly-sized room that opens to two medium-sized rooms, and with the right movie the floors literally shake so I doubt you’d have a problem with the “enough” part.  You don’t really give enough detail to go any further than that though.  FWIW. 

Room layout dictates I can't have more than one sub.

Blast that room dictator! Who does he think he is to tell you what you can and cannot do? Oh well. We get the government we deserve, I guess is true after all.

Blast that room dictator! Who does he think he is to tell you what you can and cannot do?

Yeah, he’s a bad dude just like his evil brother the cabinet dictator.  Really hate that guy too.  Lest we not forget the mother of them all — the wife dictator.  Dedicated rooms and divorce are the best weapons we audiophiles have against such injustice.  Yeah they’re expensive, but you get what you pay for. 

Buy2 subs it equals out 60 hz nulls in the room
best sub by far and you can get  for under $2k delivered,for 2.
free shipping 45 day audition and free return if not satisfied with a great app the most high tech 13 inch to below 18 HZ ,and 5 year warranty with a Transferrable warranty ,Check it out 
sub of the year the SVS 3000 SB ,and is a smaller version of the great ultra 16 sub, Ano other sub has a Dual pole piece meaning even at low volume tuneful Bass . I bought them last year and I owned several $1500-$2k + subs 

My room is similar in dimensions to yours. "Enough"? That depends on how much thundering bass you want. A room of that size must be able to accommodate at least a second sub. Don't predetermine where a second sub must go. Sub placement is one of the the most critical parts of the deal. Surely, your room size and geometrical dimensions can allow for the addition of at least a second box.

Example....In my room, equal in size to yours, I use a pair of bookshelf speakers on stands and a pair of 10" subs. Fills my bill perfectly. My listening is primarily music rather than HT. If you're unsure whether one sub is enough start with one. See how it works. A second sub can be added later. But, don't obsess about the size of the sub speaker. Focus on the placement of it/them. If music, movies, or both are your preference that will guide you in one direction or another.

I have benefited from millercarbon's suggestions about subs and other things. I would ask him directly what results you want to obtain.

Just bear in mind that not all 12 inch subs are created equal.  I also recommend SVS, they are built like tanks.  I use a SB-2000 (12" woofer) in a room similar to the OP's and have to keep the sub's volume around half way to stop my woman's ornaments from rattling off shelves.  I also use a SB-1000 nearfield under my computer desk where it doubles as a footstool and it serves both purposes quite nicely.

You should really use 2.
Not ported. 
If your on hardwood isolate them with upgraded feet.
Have them come in about 20 Hz above where your speaker's give out.

I've used 2 x 18" Eminence Kilomax drivers is 14 cu ft sealed cabinets in a room of similar volume.  EQ'ed the subs and placed them in the corners behind the main speakers.  Works OK. 

It all depends on the listening position in the room.  The optimum listening position and main speaker position may not be the optimum listening position for the subs.   

The answer to your question is NO.  Get four subs...it will be for the best.

I have a similar room; using JBL pro stage 18" powered sub, located on the back wall, firing sideways.  No complaints.

My living room is an open floor plan like yours with a 2 story cathedral ceiling. I have an older SVS 2039pc+ (12” driver with 500w amp) that produces plenty of earth shattering low bass. I use a Dspeaker Antimode 8033c to tame the peaks and take away room nodes. The improvement is very noticeable with cleaner multi-note bass. Instead of multiple subs get one very good sub and the 8033c.

http://www.dspeaker.com/en/products/anti-mode-8033.shtml

+1 ebanksms
When I compared a JL Audio F113 to my Velodyne DD-18 it was every bit as potent. At the time the newer JL seemed to have a better cabinet along with a proprietary driver. It's auto only ARO room correction was limiting. 

If you're able to crawl test and position a sub of similar quality and equalization you can expect very good performance at the listening position from a 10".
With this level of subwoofer adding a non equalized extension sub interconnected to the main sub and positioned at the rooms second largest mode will further reduce the rooms modes and maintain equalization.  

I am lucky.  I have a dedicated room.  I was very impressed by room treatments improving my bass.  I have 2-10" subs.  I don't think size matters as much as being able to have multiples and treatment.  It helps every aspect of the music.  I know, this could be a moot point in your case.  So if you walk around the room and hear peaks and valleys in bass and you cant do at least one (multiple or treat) try moving sub around. 

Depends on what you listen to and how loud you listen to it.

I have a 10 x 14 x 9 room and a 4 sub dba made up of three different brands; 2-13" subs and 2-12" subs. I don't listen real loud very often but on occasion I have pushed the room to 105 db plus and in doing so I have driven one of the subs, a Rythmik F12, into thermo overload twice. Is there a problem with the Rythmik you might ask? Maybe, but Rythmik did't think so. Am I a bass head/hog? When the music calls for it; absolutely. Am I completely crazy? No question, but the moral of the story is, It depends. Know your tendencies and what you are looking for and remember, the bigger the room the harder it is to fill.

I agree that sub location is critical, but only if you have options. If you can only put the sub in one place, that is where it has to go. I have one tucked under an end table and another behind the sofa. Are these the best locations for these subs? I have no idea, these were the only places I could put them, but the room does sound better with them than without them.

is this for 2 channel or home theater? People tend to way over do bass in a 2 channel setup. I want to hear a tight every note detected bass not a muddy rattle the windows. Then with my home theater I do want to rattle the windows.

That's a good sized room.  Even if you went with a larger sub I would probably add a second one to the mix.
Depends on which sub and what type of bass you are looking for too.  Music, Home Theater, combo of both.....etc.

I'm using an SVS SB2000 (sealed box) sub in a 320 square foot room with 8' ceilings, in a 2.1 stereo application. This sub is more than adequate for this application. Room placement will be important.

I ended up buying the SVS wireless adapter for the sub, and playing around with room placement for a few weeks until I found the spot where it sounded best to me, and blended well with my mains.

If I could do it all over though, I would go with 2 smaller / identical subs like many people are recommending.

One sub, ok Tekton 21" bass bin (sub) it has two M/B couplers in it to...

Great box  25 to 300 or so,, 95% + sensitive. 

Regards..

In my limited (only) experience, one subwoofer added the LFE to the movies, but the low bass was localized to the left side of the room. The subwoofer was behind the left speaker. With two subwoofers, the LFE seems to come from all around the room. My vote, at least two. Some folks have recommend four.

I have not read all the posts but:
Will 12 inch subwoofer be enough for an 18x20 room (with 10 ft cielings)
 
In short: no it will not.

Most of us has not since 1933 we know that if you want to be able to HEAR a sinus wavelength at 20Hz when you play at normal 80 db @ 1000 hz. Then you need to play the at 20 hz @ 120 db (!).

So when we study the graphs over what our ears are able to hear and at what sound pressure that is needed to have for us to be able to hear it.
https://en.m.wikipedia.org/wiki/Equal-loudness_contour

So the solution is much more cone area is needed and power. Then let a DSP mimic the courve in the link above. Then it is "enough".

I am in progress to building 2 18" that will perhaps rather close to the listening area and my miniDSP will help me. Maybe I will reach my goal. (Oh and it is OB that is another problem with that low efficiency).

My room i6 16 X 30 with an open concept like yours. I use 4 12" subwoofers. You will need at least two. With one you risk overloading it if you play stuff like pipe organs. 

I have both JL and REL in two systems.  By far the REL disappears and the bass is seamless.  That said, I have a 30x30 x9 ft room and 1 S12 greatly improved the sound paired with 802D's.  I added second S812 as a stereo pair and it resulted in another level of improvement.  I personally would either stack a second S812 or get the S212 given the size of your room.  Hope that helps.

I use an Aerial SW12 in a large room.  I will not be upgrading any time soon.  So far, very happy!

It depends on your expectations, your mains & other factors. I will describe my 2 rooms and comment on each.

Room 1, 17.5’ x 24’, the ceiling is 9’ at the sides and 14’ in the center. There is an entry to a dining room and small hall that cannot be closed off. Subwoofer is a meager 10" 50 watt. Mains have two 7" drivers each. I was quite surprised with how well the sub did in this rooms volume. I considered this sub weak in every other room I placed it in before (and with every other pair of mains). I listen to TV and 2 channel music in this room. The bass frequency is not level everywhere in the room. More importantly, I found a location for the single sub that provides good response in the two primary sitting locations, the dinner table and the couch centered in front of the TV (I can survive 5 seconds of imbalance when entering & leaving the room). I might eventually build and try out four 12" DIY subs because I already have the drivers from a previous project. I don’t feel any urgency since bass is already adequate in this scenario.

Room 2, 15’ x 22’ x 9’ ceiling (much less volume than room 1). I can close all the doors. This is the home theater room with a 12" custom built sub tuned to 20Hz. My bass expectation is higher in this room since it is 7.1 with LF effects output. The sub is excursion limited at 150-300 watts. My expectation is not met in this room so I am currently building two cabinets for 18" drivers with 32mm excursion, they will be tuned to 14Hz and leveled with a mini DSP. In this room I expect to feel the bass below 20Hz whether I can hear it or not.

Hopefully you can place your expectations and situation relative to my two examples.