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\section{Abstract}  Various MHD (magnetohydrodynamic)  equilibrium tools, some of which being recently developped or updated, are used on the medium-size COMPASS tokamak. tokamak \cite{P_nek_2006}.  MHD equilibrium is a fundamental property of the tokamak plasma. Its knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpretting and plannig tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code [?], the free-boundary equilibrium code FREEBIE [?], and the rapid plasma boundary reconstruction part of the EQUINOX code [?]. We demonstrate that FREEBIE can determine the equilibrium and corresponding poloidal field (PF) coils currents from a for  given plasma boundary. parameters.  Both EFIT++ and EQUINOX can reconstruct the equilibrium from synthetic diagnostic data (with an artificial noise) from FREEBIE. Optimum reconstruction parameters are estimated; in addition, possible enhancements using more diagnostics are discussed and simulated using synthetic diagnostics.  The accuracy of the reconstruction depends on the noise level and certain numerical parameters. For example, EFIT++ reconstruction with a low-order $p'\left(\psi\right)$ and $ff'\left(\psi\right)$ is not perfect even with no noise. The recent EFIT++ version 6 is several times faster compared to version 4.