Communities like Googology Wiki and the “Large Number Contest” use FGH as a standard ruler. “My number is at level ( f_\psi(\Omega_\omega)(n) )” is a precise claim. A calculator lets you compare ( f_\Gamma_0(3) ) vs ( f_\varphi(2,0,0)(4) ).
Standard definitions for fundamental sequences (using the Wainer Hierarchy) include: fast growing hierarchy calculator