An integral formulation of pinch equilibrium gives kinetic pressure profiles for plasmas with cylindrical symmetry. This simplified method offers an alternative to solving the Grad-Shafranov equation and leads to closed-form expressions obtained analytically. Results include the explicit dependence of equilibrium on the externally-generated field B0, and field reversal appears as an intrinsic feature of screw-pinches. Basic insight into Z-pinches, screw-pinches, and (F, theta ) relations comes from the same formalism.