  The force-free parameter $\alpha$, also known as helicity parameter or twist
parameter, bears the same sign as the magnetic helicity under some restrictive
conditions. The single global value of $\alpha$ for a whole active region gives
the degree of twist per unit axial length. We investigate the effect of
polarimetric noise on the calculation of global $\alpha$ value and magnetic
energy of an analytical bipole. The analytical bipole has been generated using
the force-free field approximation with a known value of constant $\alpha$ and
magnetic energy. The magnetic parameters obtained from the analytical bipole
are used to generate Stokes profiles from the Unno-Rachkovsky solutions for
polarized radiative transfer equations. Then we add random noise of the order
of 10$^{-3}$ of the continuum intensity (I$_{c}$) in these profiles to simulate
the real profiles obtained by modern spectropolarimeters like Hinode (SOT/SP),
SVM (USO), ASP, DLSP, POLIS, SOLIS etc. These noisy profiles are then inverted
using a Milne-Eddington inversion code to retrieve the magnetic parameters.
Hundred realizations of this process of adding random noise and polarimetric
inversion is repeated to study the distribution of error in global $\alpha$ and
magnetic energy values. The results show that : (1). the sign of $\alpha$ is
not influenced by polarimetric noise and very accurate values of global twist
can be calculated, and (2). accurate estimation of magnetic energy with
uncertainty as low as 0.5% is possible under the force-free condition.
