In this article, fast and simple closed-form relations are presented to calculate input impedance of filamentary-excited printed narrow slot antenna on electrically thin dielectric substrate near to half wavelength resonance frequency. This antenna is a complementary structure of thin printed dipole antenna. The obtained formulations have been verified numerically by a commercially available full-wave electromagnetic simulator and then a prototype antenna has been produced. Experimental measurements are realised on the antenna and these measurement values of input impedance also have verified analytical relations and numerical simulations. It is shown that analytical, numerical and experimental results are close to each other. Therefore, these relations can be utilised as an initial design step just before making detailed numerical analyses. Besides, the given relations can be easily realised in CAD-oriented platforms for fast calculations.