The electronic spectrum of carbon chains has not been well understood in nature and deserves further study. In the present work, (time-dependent) density functional theory [(TD-)DFT] was employed to investigate the geometric and electronic structures as well as the allowed 11Σu+ ← X1Σg+ electronic transition of the H-capped carbon chains H-(C≡C)n-H (n = 3-9). The calculated geometric parameters and vertical excitation energy are perfectly consistent with the known experimental observations. The size dependence of electronic and optical characteristics in carbon chains is explained in depth by wavefunction analysis for electronic excitation and paid special attention to through data fitting and extrapolation, whose accuracy is confirmed by the specified species with n = 15. The suggested extrapolation formulas allow estimating the behavior of the electronic and optical properties for increasing chain length and even obtaining the limit values for sp-hybridized carbon allotrope carbyne.