It depends! I'm sorry, I know you are tired of hearing that, but it's true. The Social Security Administration (SSA) will probably find you disabled if 1) you are not engaging in Substantial Gainful Activity (working and earning more than a certain amount of money per month); 2) you have a severe impairment or combination of impairments that is expected to last 12 months or more or is expected to end in death; and 3) you meet or equal one of the SSA's listings; or 1) & 2) and 4) can't perform any of your relevant previous jobs; and 5) can't perform any other job that is available to you in significant numbers in the national economy, based on your age, education level, and job skills. Also, drug and/or alcohol abuse cannot be a material factor in your disability. This is a general description of the disability standard which leaves out several rules and exceptions but is an excellent starting point for someone to determine whether he/she is disabled according to Social Security.
So back to you. You were a carpenter, but severe back pain has prevented you from making your usual woodworking magic. Sadly this is a common situation! Gone are the days when someone can do a physically demanding job for a reasonable number of years then retire with a pension. Nowadays the average American has to work until they drop! And it sounds like you have indeed dropped. First, you may not be disabled if you took another kind of job. No matter that you can't be a carpenter anymore, if you are working at another job for more than SGA then the SSA will almost surely find you not disabled. Second, if your back pain is expected to last more than 12 months or result in death (I'm guessing not, but who knows?) then the SSA may find you disabled, but you must also pass 3) or 4) and 5). It is unlikely that you meet a listing, not may people do, but you can look at them here. There are special rules between 3) and 4) that I won't get into but you can read about them here. So that leaves 4) and 5), and you have to pass both to be disabled if you don't pass 3). It is clear that you can't work as a carpenter anymore, but have you done another kind of job in the 15 years before you became disabled? If you can do any of your previous relevant employment, SSA will likely find you not disabled. If not, we can go to 5).
I could write a whole book on the dreaded "Step Five" which would instantly put you to sleep. It is a complex and confusing subject. To put it simply: you are a 52 year old ex-carpenter, and people over 50 are in a favored class according to the "Step Five" rules. The SSA will probably find you disabled if you have no recent education that would lead to skilled work or relevant, transferable work skills, and are limited to sedentary work. Confused? You're not the only one. The staff members at the SSA often do not know the rules very well. So if you get denied, don't give up! A good lawyer can help tremendously.
Disclaimer: This post is not meant to be legal advice, it is for informational purposes only, and any similarity to a reader's case is purely coincidental.