In this paper, a variety of analytical/integral methods are compared for calculating the axial force between a cylindrical magnet and a “thick” solenoid that consists of many turns both radially and axially. Two newly developed techniques are introduced: one being numerical integration-based and the other completely analytical. These are compared to two other techniques, each shown to have various advantages in different contexts. One method in particular is introduced that is shown to be the most computationally efficient in the majority of actuator designs. This method is then used to optimize a typical “sleeve-type” magnet-coil actuator based on the cost function of peak force, and it is shown that optimal values of wire thickness and magnet-coil geometry can be chosen based on desired coil impedance and magnet volume.