value is the amount (of money or goods or services) that is considered to be a fair equivalent for something else worth is An indefinite quantity of something having a specified value. cowboy...

The terms are largely equivalent in their noun forms. "Value" is a borrowing from French, whereas "worth" is of Saxon derivation. As verbs, however, they work quite differently (note that "worth" is not a verb by itself but is part of phrasal verbs such as "to be worth") (x)is worth $(y). = (x) has a value of $(y). = (x) is valued at $(y). I value (x). = I find worth in (x) = I believe (x) has worth.