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We present a study of the Fermi surface of KFe$_2$As$_2$ single crystals.Quantum oscillations were observed in magnetostriction measured down to 50 mKand in magnetic fields $H$ up to 14 T. For $H \parallel c$, the calculatedeffective masses are in agreement with recent de Haas-van Alphen and ARPESexperiments, showing enhanced values with respect to the ones obtained fromprevious band calculations. For $H \parallel a$, we observed a small orbit at acyclotron frequency of 64 T, characterized by an effective mass of $\sim 0.8m_e$, supporting the presence of a three-dimensional pocket at the Z-point.

Fermi Surface of KFe$_2$As$_2$ from Quantum Oscillations in Magnetostriction