linguistic:paraphrasing
History and definition

The concept of natural units was introduced in 1874, when George Johnstone Stoney, noting that electric charge is quantized, derived units of length, time, and mass, now named Stoney units in his honor. Stoney chose his units so that G, c, and the electron charge e would be numerically equal to 1. In 1899, one year before the advent of quantum theory, Max Planck introduced what became later known as the Planck constant. At the end of the paper, he proposed the base units that were later named in his honor. The Planck units are based on the quantum of action, now usually known as the Planck constant, which appeared in the Wien approximation for black-body radiation. Planck underlined the universality of the new unit system, writing:

... die Möglichkeit gegeben ist, Einheiten für Länge, Masse, Zeit und Temperatur aufzustellen, welche, unabhängig von speciellen Körpern oder Substanzen, ihre Bedeutung für alle Zeiten und für alle, auch ausserirdische und aussermenschliche Culturen nothwendig behalten und welche daher als »natürliche Maasseinheiten« bezeichnet werden können.

... it is possible to set up units for length, mass, time and temperature, which are independent of special bodies or substances, necessarily retaining their meaning for all times and for all civilizations, including extraterrestrial and non-human ones, which can be called "natural units of measure".

Planck considered only the units based on the universal constants G {\displaystyle G}, h {\displaystyle h}, c {\displaystyle c}, and k B {\displaystyle k_{\rm {B}}} to arrive at natural units for length, time, mass, and temperature. His definitions differ from the modern ones by a factor of 2 π {\displaystyle {\sqrt {2\pi }}}, because the modern definitions use ℏ {\displaystyle \hbar } rather than h {\displaystyle h}.

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 the Coulomb constant k e {\displaystyle k_{\text{e}}} is added to the list of constants used by Planck. Thus, this charge unit is typically given by q P = 4 π ϵ 0 ℏ c ≈ 1.875546 × 10 − 18 C ≈ 11.7 e. {\displaystyle q_{\text{P}}={\sqrt {4\pi \epsilon _{0}\hbar c}}\approx 1.875546\times 10^{-18}{\text{ C}}\approx 11.7\ e.}

In SI units, the values of c, h, e and k are exact and the values of ε and G in SI units respectively have relative uncertainties of 1.6 × 10 and 2.2 × 10. Hence, the uncertainties in the SI values of the Planck units derive almost entirely from uncertainty in the SI value of G.

Compared to Stoney units, Planck base units are all larger by a factor 1 / α ≈ 11.7 {\textstyle {\sqrt {{1}/{\alpha }}}\approx 11.7}, where α {\displaystyle \alpha } is the fine-structure constant.