We introduce the notion of a rank function on a \((d+2)\) -angulated category \(\mathcal {C}\) which generalises the notion of a rank function on a triangulated category. Inspired by work of Chuang and Lazarev, for \(d\) an odd positive integer, we prove that there is a bijective correspondence between rank functions defined on objects in \(\mathcal {C}\) and rank functions defined on morphisms in \(\mathcal {C}\) . Inspired by work of Conde, Gorsky, Marks and Zvonareva, for \(d\) an odd positive integer, we show there is a bijective correspondence between rank functions on \({\textsf{proj}}A\) and certain additive functions on \({\textsf{mod}}({\textsf{proj}}A)\) , where \(A\) is a twisted \((d+2)\) -periodic algebra and \({\textsf{proj}}A\) is endowed with the Amiot-Lin \((d+2)\) -angulated category structure. This allows us to show that every integral rank function on \({\textsf{proj}}A\) can be decomposed into a (locally finite) sum of irreducible rank functions.
