Trapped ion mobility spectrometry (TIMS) is a relatively new gas-phase separation method that has been coupled to quadrupole orthogonal acceleration time-of-flight mass spectrometry. The TIMS analyzer is a segmented rf ion guide wherein ions are mobility-analyzed using an electric field that holds ions stationary against a moving gas, unlike conventional drift tube ion mobility spectrometry where the gas is stationary. Ions are initially trapped, and subsequently eluted from the TIMS analyzer over time according to their mobility (K). Though TIMS has achieved a high level of performance (R > 250) in a small device (<5 cm) using modest operating potentials (<300 V), a proper theory has yet to be produced. Here, we develop a quantitative theory for TIMS via mathematical derivation and simulations. A one-dimensional analytical model, used to predict the transit time and theoretical resolving power, is described. Theoretical trends are in agreement with experimental measurements performed as a function of K, pressure, and the axial electric field scan rate. The linear dependence of the transit time with 1/K provides a fundamental basis for determination of reduced mobility or collision cross section values by calibration. The quantitative description of TIMS provides an operational understanding of the analyzer, outlines the current performance capabilities, and provides insight into future avenues for improvement.