The theory behind solving for three-dimensional forces is closely related to that of solving for two-dimensional forces.

The equation for equilibrium is

     ΣF = 0

For three dimensions, this can be expanded to

     ΣF = ΣF_xi + ΣF_yj + ΣF_zk = 0

For the expanded equation, each of the three directions must be equal to zero, giving

     ΣF_x = 0
     ΣF_y = 0
     ΣF_z = 0

The equilibrium equation has been separated into three components corresponding to the x, y, and z axes. Since each equation is independent of the others, the equations can be used to determine up to three unknowns.