Since its introduction over 40 years ago algebraic K-theory, which provides powerful invariants, still remains hard to compute. The subject of this work is the construction of an isomorphism between relative algebraic K-groups and relative algebraic cyclic homology in low dimensions, for certain nilpotent ideals. This isomorphism generalizes the Theorem of Goodwillie [Goo86] concerning rational algebras and provides a more accessible alternative to topological cyclic homology for the computation of algebraic K-groups.