The Rogowski coil (RC) is a low-cost current sensor particularly suited for high-frequency transient diagnostics, including the detection of partial discharge (PD) in high-voltage power equipment. This article presents 3-D modeling and design of RC for pulsed current (PC) signal measurement. In the development of RC prototype, selecting the appropriate terminating resistance is crucial to calibrate its response accurately for measuring PC signal. The terminating resistance effect on the coil model is analyzed through three methodologies such as analytical, finite element method (FEM) simulation, and experimental investigations. This article extensively deliberates the modeling of the 3-D structure of the RC in Ansys Maxwell and the development of an RC hardware prototype in the laboratory. The prototype-designed RC is tested for measuring PC signal of 100 and 200 mA (peak) with different terminal resistances. The electrical parameters of the RC are determined through simulation, exhibiting a close match with the measured values. The output voltage estimation of RC is performed, analyzed through three methods, and its results are reported. The comparison of RC results indicates a good match, affirming the validity of the RC design for PC measurement applications across all methodologies. The coil sensitivity is calculated and compared through analytical, FEM, and experimental results, focusing particularly on the peak PC signal with different terminal resistances. Furthermore, the frequency response analysis for RC has been investigated and its results are reported.