Is learning to code worth it? (thinking about possible coding careers)

I've read on many places online that it is possible to teach yourself how to code or computer program. I assume, though, that doing so would actually take a significant amount of time and effort. Since I can't afford to go back to school to learn coding at a university, I have thought about teaching myself how to code instead. However, I only want to do it if it could lead to a career. But, how do you get a career in coding if you are completely self-taught? How would you convince a company to hire you if you are self-taught?