This study proposes a method for calculating back electromotive force and force waveforms in air-core linear permanent-magnet synchronous motors. To obtain an accurate air-gap magnetic field distribution, adequate boundary conditions must be applied to solve Poisson's equation. Faraday's law and Lorentz force equation can be used to derive the equations for back EMF and force waveforms and thus determine the corresponding waveforms. The proposed equations are applicable to linear motors with identical structures, and the analysis results can be quickly obtained by substituting related parameters into the equations. The presented methods were verified using finite element method and experimental results.