We　consider　capacitated　k-means　clustering　whose　object　is　to　minimize　the　within-cluster　sum　of　squared　Euclidean　distances.　The　task　is　to　partition　a　set　of　n　observations　into　k　disjoint　clusters　satisfying　the　capacity　constraints,　both　upper　and　lower　bound　capacities　are　considered.　One　of　the　reasons　making　these　clustering　problems　hard　to　deal　with　is　the　continuous　choices　of　the　centroid.　In　this　paper　we　propose　a　discretization　algorithm　that　in　polynomial　time　outputs　an　approximate　centroid　set　with　at　most　fractional　loss　of　the　original　object.　This　result　implies　an　FPT(k,d)　PTAS　for　uniform　capacitated　k-means　and　makes　more　techniques,　for　example　local　search,　possible　to　apply　to　it.　©　2020,　Springer　Nature　Switzerland　AG.