We explore coherent ergotropy extraction in quantum batteries from a resource-geometric point of view. For an initial state ρ, we quantify the coherent extraction process by the coherent ergotropy Ec(ρ) and the coherent extraction distance D[ext]c [(][ρ][)] between the active state σρ and the passive state Pρ. This defines the geometric power capacity Πc(ρ) = Ec(ρ)/D[ext]c [(][ρ][)], which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying ∥Vt∥≤ ν, the actual coherent discharging power is bounded by P[ext]c [(][ρ][;][ V][t][)] ≤ νΠc(ρ), showing that Πc(ρ) is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on Πc(ρ) are derived by combining relative entropy bounds on coherent ergotropy with geometric bounds on the coherent extraction distance. We also formulate coherence measure induced bounds and protocol-corrected capacities involving the effective speed of a given Hamiltonian. Qubit and qutrit examples demonstrate that Πc(ρ) captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.