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Abstract  We generalize the Caldero–Chapoton formula for cluster algebras of finite type to the skew‐symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over certain Iwanaga–Gorenstein algebras introduced in [Geiß, Leclerc and Schröer,  Invent Math . 209 (2017) 61–158]. The proof relies on the realization of the positive part of the enveloping algebra of a simple Lie algebra of the same finite type as a convolution algebra of constructible functions on representation varieties of   H  , given in [Geiß, Leclerc and Schröer,  Represent. Theory  20 (2016) 375–413]. Along the way, we obtain a new result on the PBW basis of this convolution algebra.

Quivers with relations for symmetrizable Cartan matrices V: Caldero–Chapoton formulas