Explicit and closed-form expressions describing magnetic behaviors of uniaxial magnetic materials are derived. Explicit and closed-form expressions for magnetic torque, magnetization orientation, and thier derivative functions with respect to the intensity and the orientation of an applied field. Those explicit expressions could give elegant mehtods of measuring magnetic anisotropy and saturation magnetization by the least squre fitting. In addition, on could use them to study the distribution function of magnetic propeties of a non-interacting magnetic aggregate.