The Qweak experiment at Thomas Jefferson National Accelerator Facility (Jefferson Lab) will measure the proton's weak charge by measuring the parity violating asymmetry in elastic electron-proton scattering at very low momentum transfer, with the aim of determining the proton's weak charge with 4% combined statistical and systematic errors. The experimental apparatus includes a longitudinally polarized electron beam, a liquid hydrogen target, a room temperature toroidal magnetic spectrometer, and a set of precision detectors for the scattered electrons. The toroidal magnetic spectrometer, which will deflect away the inelastic scattered electrons and focus the elastic scattered electrons onto the detectors, plays a crucially important role in the experiment. In this thesis, in order to meet the requirements for the installation and calibration of the toroidal magnetic spectrometer, the numerical simulation of the spectrometer's magnetic field based on a realistic magnet model is discussed, a precise 3D field mapping is introduced, and some simulation results are provided. The zero-crossing analysis technique, which can be used to precisely infer the individual coil locations of the toroidal magnet, is presented and explored in detail.