Planck Base Units

This Base Planck Units table is from Wikipedia. It is Table 2 within this linked article.

Base Planck units
NameDimensionExpressionValue (SI units)
Planck lengthLength (L)l_{\text{P}}={\sqrt {\frac {\hbar G}{c^{3}}}}1.616 229(38) × 10−35 m[6]
Planck massMass (M) m_{\text{P}}={\sqrt {\frac {\hbar c}{G}}}2.176 470(51) × 10−8 kg[7]
Planck timeTime (T)t_{\text{P}}={\frac {l_{\text{P}}}{c}}={\frac {\hbar }{m_{\text{P}}c^{2}}}={\sqrt {\frac {\hbar G}{c^{5}}}}5.391 16(13) × 10−44 s[8]
Planck chargeElectric charge (Q){\displaystyle q_{\text{P}}={\sqrt {4\pi \varepsilon _{0}\hbar c}}={\frac {e}{\sqrt {\alpha }}}}1.875 545 956(41) × 10−18 C[9][10][11]
Planck temperatureTemperature (Θ)T_{\text{P}}={\frac {m_{\text{P}}c^{2}}{k_{\text{B}}}}={\sqrt {\frac {\hbar c^{5}}{Gk_{\text{B}}^{2}}}}1.416 808(33) × 1032 K[12]

The key equation:

Particularly focused here:

planckclengthtimex
  1. That equation generated the 10th line in the horizontally-scrolled chart.
  2. It engendered a notation by notation analysis which is very much a working project.
  3. It has engendered an ongoing analysis.