Unlike the case with the International System of Units, there is no official entity that establishes a definition of a Planck unit system. Some authors define the base Planck units to be those of mass, length and time, regarding an additional unit for temperature to be redundant. Other tabulations add, in addition to a unit for temperature, a unit for electric charge, so that either the Coulomb constant k e or the vacuum permittivity ϵ ϵ 0 is normalized to 1. Thus, depending on the author's choice, this charge unit is given by q P = 4 π π ϵ ϵ 0 ℏ ℏ c ≈ ≈ 1.875546 × × 10 − − 18 C ≈ ≈ 11.7 e for k e = 1 , or q P = ϵ ϵ 0 ℏ ℏ c ≈ ≈ 5.290818 × × 10 − − 19 C ≈ ≈ 3.3 e for ε ε 0 = 1 . Some of these tabulations also replace mass with energy when doing so.