Capacitance-based damage self-sensing and the in-plane electric permittivity of continuous carbon fiber polymer-matrix composite are unprecedentedly reported. Capacitance-based self-sensing is advantageous over previously reported electrical-resistance-based self-sensing in not needing intimate electrical contacts and that two (rather than four) contacts suffice. Using a 220 x 220-mm(2) unidirectional one-lamina polyamide-6-matrix composite, the capacitance (2 kHz) is measured in the through-thickness and in-plane directions using 25 x 25-mm(2) aluminum-foil electrodes that are sandwiching and coplanar, respectively. Due to the composite's conductivity and the LCR meter's limitation, a dielectric film (adhesive tape) is positioned between electrode and specimen. In practice, this film can be the paint on the composite. Judiciously positioned artificial damage (1.1-mm diameter through-holes) causes the through-thickness capacitance to increase monotonically and the in-plane capacitance to decrease monotonically with increasing damage, due to the effect of the damage on the fringing electric field. The relative permittivity is 2160 +/- 510 and 1640 +/- 330 for the longitudinal and transverse directions, respectively, with anisotropy 1.3. The DC resistivity is 0.0072 +/- 0.0004 and 10.9 +/- 0.9 Omega cm in the longitudinal and transverse directions, respectively, with anisotropy 1500. The conductivity controls the current spreading, while the high permittivity provides the capacitance effect. The resistivity anisotropy causes the dependence of the capacitance-based sensing on the fiber orientation. (C) 2018 Elsevier Ltd. All rights reserved.