The establishment of the mid-infrared and terahertz free-electron laser (MIR/THz FEL) facility is ongoing at the PBP-CMU Electron Linac Laboratory (PCELL) in Chiang Mai University. The facility utilizes an S-band radio-frequency (RF) gun and a linear accelerator (linac) to generate and accelerate electron bunches. These electron bunches are accelerated in the RF gun and the linac using RF pulses with a frequency of 2856 MHz. Measuring the RF properties becomes essential, as the RF pulse information can be utilized to estimate the electron beam properties. To achieve the measurement results, we employed an RF measurement system comprising directional couplers, coaxial cables, attenuators, a crystal detector, and an oscilloscope. Prior to conducting measurements, the crystal detector and RF equipment were calibrated and characterized to ensure precise and reliable results. The electron beam energy estimation using the measured RF power was compared with the measured beam energies. The gun and the linac were operated with an absorbed RF power of 1.52 MW and an input power of 1.92 MW, respectively. The estimated electron beam energies were found to be 2.18 MeV and 15.0 MeV, respectively, closely aligning with the measured beam energies of 2.1 MeV and 14.0 MeV after the gun and linac acceleration. These consistent energy values support the reliability of our RF power measurement system and procedure.