  $f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to
general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity
with fixing the coincident gauge condition. Using the standard Dirac-Bergmann
algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This
result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is
completely broken due to the gauge fixing. Moreover, in terms of the
perturbations, we discuss the possible mode decomposition of these degrees of
freedom.
