This paper explores heights of posets formed by Green's relations on semigroups. It focuses on stable semigroups, proving equalities between L-, R-, J- and H-heights. Main results: for a stable semigroup with L-height n, the R-height and J-height are between n and 2^n - 1, with examples realizing these bounds. Also if L- and R-heights are at least 2, the J-height is bou...