Detection of motion with parallel plate capacitors is commonly used in MEMS; small amplitude of motion is typically assumed. In this paper, we derive precise and constructive equations for the case of parallel plate capacitive detection of arbitrary amplitude of motion. These equations are solved in closed form without using a small displacement assumption. A precise relation between the amplitude of the mechanical motion and the amplitude of the electrical sensing signals is obtained, which allows us to eliminate the nonlinearity error of parallel plates. To illustrate the theoretical findings, MEMS test structures were designed and fabricated. Experiments confirm the developed theory. The formulated algorithms of detection are especially valuable for capacitive detection of large amplitudes of periodic motion in dynamic MEMS sensors and actuators.