  In fusion plasmas, where electron temperatures $T_e$ range from keV to
hundreds of keV, Bremsstrahlung radiation constitutes a significant energy loss
mechanism. While various thermal average fitting formulas exist in the
literature, their accuracy is limited, particularly for $T_e \leq 20$ keV with
error $>10\%$. Additionally, non-relativistic fitting formulas become invalid
for $T_e \geq 50$ keV. The accurate calculation of Bremsstrahlung radiation is
important for fusion gain study, especially of advanced fuels fusion. In this
work, we develop new but still simple fitting formulas that are valid for
electron temperatures ranging from small ($\lesssim0.1$ keV) to extreme
relativistic range, with errors of less than 1\% even for high atomic number
ions (e.g., $Z=30$), which could be sufficient for fusion plasma applications.
Both electron-ion (e-i) and electron-electron (e-e) Bremsstrahlung radiations
are considered. Both polynomial fitting with truncated
($t=k_BT_e/m_ec^2\leq10$) and one-fit-all formulas are provided. Additionally,
we offer fitting formulas for e-i and e-e specifically for electron energies,
which could prove useful in non-Maxwellian Bremsstrahlung radiation studies.
