Description logics (DLs) are a well-known family of knowledge representation (KR) languages. The notation of DLs has the style of a variable-free first order predicate logic. In this paper a diagrammatic representation of the DL ALC– based on Peirce’s existential graphs – is presented and a set of transformation rules on these graphs provided. As the transformation rules modify the diagrammatic representation of ALC this produces a diagrammatic calculus. Some examples present in the paper illustrate the use and properties of this calculus.