This paper presents the electromagnetic design and force calculation of a compact multiaxis precision positioner. A six-coil single-moving-part platen moves over a superimposed concentrated-field permanent-magnet matrix. With a rectangular coil placed in the magnetic field generated by the superimposed concentrated-field magnet matrix, the force acting on the coil is calculated by volume integration based on the Lorentz force law. The distance between the long sides and that between the short sides of a rectangular coil are designed to be a half pitch and one pitch of the magnet matrix, respectively. This allows for the simplification of force generation and calculation, compact size, and light mass (0.64 kg) of the moving platen. Six coils are divided into three two-phase linear-motor armatures with 270 degrees or 450 degrees phase differences. The complete force-current relation for the entire platen with the six coils is derived. Experimental results are presented to verify the working principle of the positioner designed in this paper. The positioner can be employed for the stepping and scanning applications that require 3-DOF planar motions with long travel ranges in two horizontal directions and small rotational motions about the vertical axis.