This paper presents new general formulas for calculating the magnetic force between inclined circular filaments placed in any desired position. We use two approaches to calculate the magnetic force, one based on Biot-Savart law and another based on the mutual inductance between these coils. All mathematical procedures are completely described to define coil positions that lead to relatively easy method for calculating the magnetic force between inclined circular filaments in any desired position. Two formulas obtained by the simple integration of different expressions in terms of complete elliptic integrals of the first and second kind give the same numerical results. The presented methods are understandable, numerically suitable and easy applicable for engineers and physicists. We validated the new formulas through a series of examples, which are presented here.