Unità di misura di Planck derivate

Le unità di misura di Planck derivate sono quelle unità di misura derivate dalla combinazione delle unità di Planck fondamentali, come la lunghezza, la massa e il tempo.

Tabella

Unità derivate di Planck approssimate

Dimensione	Formula	Espressione		Valore, nel SI approssimata
		Versione di Lorentz–Heaviside[1]	Versione gaussiana[2][3][4][5]	Valore nel SI Lorentz-Heaviside	Valore nel SI Gaussiana
Proprietà meccanico-fisiche
Area di Planck	Area ${\displaystyle \left[L\right]^{2}}$	${\displaystyle l_{\text{P}}^{2}={\frac {4\pi \hbar G}{c^{3}}}}$	${\displaystyle l_{\text{P}}^{2}={\frac {\hbar G}{c^{3}}}}$	${\displaystyle 3,282688\cdot 10^{-69}\;m^{2}}$	${\displaystyle 2,612280\cdot 10^{-70}\;m^{2}}$
Volume di Planck	Volume ${\displaystyle \left[L\right]^{3}}$	${\displaystyle l_{\text{P}}^{3}={\sqrt {\frac {64\pi ^{3}\hbar ^{3}G^{3}}{c^{9}}}}}$	${\displaystyle l_{\text{P}}^{3}=\left({\frac {\hbar G}{c^{3}}}\right)^{\frac {3}{2}}={\sqrt {\frac {\hbar ^{3}G^{3}}{c^{9}}}}}$	${\displaystyle 1,880808\cdot 10^{-103}\;m^{3}}$	${\displaystyle 4,222111\cdot 10^{-105}\;m^{3}}$
Velocità di Planck	Velocità ${\displaystyle \left[L\right]\left[T\right]^{-1}}$	${\displaystyle v_{\text{P}}={\frac {l_{\text{P}}}{t_{\text{P}}}}=c}$		${\displaystyle 299.792.458\;{\frac {m}{s}}}$
Planck Angolare	Radiante ${\displaystyle \left[L\right]\left[L\right]^{-1}\to }$adimensionale	${\displaystyle \theta _{\text{P}}={\frac {l_{\text{P}}}{l_{\text{P}}}}=1}$		${\displaystyle 1\;\mathrm {rad} }$
Planck steradiante	Angolo solido ${\displaystyle \left[L\right]^{2}\left[L\right]^{-2}\to }$ adimensionale	${\displaystyle \theta _{\text{P}}^{2}={\frac {l_{\text{P}}^{2}}{l_{\text{P}}^{2}}}=1}$		${\displaystyle 1\;\mathrm {sr} }$
Quantità di moto di Planck	Quantità di moto ${\displaystyle \left[L\right]\left[M\right]\left[T\right]^{-1}}$	${\displaystyle m_{\text{P}}c={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{4\pi G}}}}$	${\displaystyle m_{\text{P}}c={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{G}}}}$	${\displaystyle 1,840608\;\mathrm {N} \cdot s}$	${\displaystyle 6,524785\;kg\cdot {\frac {m}{s}}}$
Energia di Planck	Energia ${\displaystyle \left[M\right]\left[L\right]^{2}\left[T\right]^{-2}}$	${\displaystyle E_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{4\pi G}}}}$	${\displaystyle E_{\text{P}}={{m}_{\text{P}}}{{c}^{2}}={\frac {\hbar }{{t}_{\text{P}}}}={\sqrt {\frac {\hbar {{c}^{5}}}{G}}}}$	${\displaystyle 5.518004\cdot 10^{8}\;\mathrm {J} }$${\displaystyle 153,278\;k\mathrm {W} \cdot h}$ ${\displaystyle 3,444067\cdot 10^{18}Ge\mathrm {V} }$	${\displaystyle 1,956081\cdot 10^{9}\mathrm {J} }$${\displaystyle 543,356\;k\mathrm {W} \cdot h}$ ${\displaystyle 1,220890\cdot 10^{28}e\mathrm {V} }$
Forza di Planck	Forza ${\displaystyle \left[M\right]\left[L\right]\left[T\right]^{-2}}$	${\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {m_{\text{P}}c}{t_{\text{P}}}}={\frac {c^{4}}{4\pi G}}}$	${\displaystyle {{F}_{\text{P}}}={\frac {{E}_{\text{P}}}{{l}_{\text{P}}}}={\frac {\hbar }{{{l}_{\text{P}}}{{t}_{\text{P}}}}}={\frac {{c}^{4}}{G}}}$	${\displaystyle 9,630908\cdot 10^{42}\;\mathrm {N} }$	${\displaystyle 1,210256\cdot 10^{44}\;\mathrm {N} }$
Potenza di Planck	Potenza ${\displaystyle \left[M\right]\left[L\right]^{2}\left[T\right]^{-3}}$	${\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{4\pi G}}}$	${\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {c^{5}}{G}}}$	${\displaystyle 2,887274\cdot 10^{51}\;\mathrm {W} }$	${\displaystyle 3,628255\cdot 10^{52}\;\mathrm {W} }$
Intensità radiante di Planck	Intensità angolare ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-3}}$	${\displaystyle {\frac {P_{\text{P}}}{\theta _{\text{P}}^{2}}}={\frac {c^{5}}{4\pi G}}}$	${\displaystyle \iota _{\text{P}}={\frac {P_{\text{P}}}{\theta _{\text{P}}^{2}}}={\frac {c^{5}}{G}}}$	${\displaystyle 2,887274\cdot 10^{51}\;{\frac {\mathrm {W} }{\mathrm {sr} }}}$	${\displaystyle 3,628255\cdot 10^{52}\;{\frac {\mathrm {W} }{\mathrm {sr} }}}$
Intensità di Planck	Intensità ${\displaystyle \left[M\right]\left[T\right]^{-3}}$	${\displaystyle i_{\text{P}}={\frac {P_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{8}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle i_{\text{P}}=\rho _{\text{P}}^{E}c={\frac {P_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{8}}{\hbar G^{2}}}}$	${\displaystyle 8,795455\cdot 10^{119}\;{\frac {\mathrm {W} }{m^{2}}}}$	${\displaystyle 1,388923\cdot 10^{122}\;{\frac {\mathrm {W} }{m^{2}}}}$
Densità di Planck	Densità ${\displaystyle \left[M\right]\left[L\right]^{-3}}$	${\displaystyle \rho _{\text{P}}={\frac {m_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {\hbar \,t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle \rho _{\text{P}}={\frac {m_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {c^{5}}{\hbar G^{2}}}}$	${\displaystyle 3,264346\cdot 10^{94}\;{\frac {kg}{m^{3}}}}$	${\displaystyle 5,154849\cdot 10^{96}\;{\frac {kg}{m^{3}}}}$
Densità energetica di Planck	Densità di energia ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-2}}$	${\displaystyle u_{\text{P}}={\frac {E_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle u_{\text{P}}={\frac {E_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {c^{7}}{\hbar G^{2}}}}$	${\displaystyle 2,933848\cdot 10^{111}\;{\frac {\mathrm {J} }{m^{3}}}}$	${\displaystyle 4,632947\cdot 10^{113}\;{\frac {\mathrm {J} }{m^{3}}}}$
Frequenza angolare di Planck	Frequenza ${\displaystyle \left[T\right]^{-1}}$	${\displaystyle \omega _{\text{P}}={\frac {\theta _{P}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{4\pi \hbar G}}}}$	${\displaystyle \omega _{P}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}\;}$	${\displaystyle 5,232458\cdot 10^{42}{\frac {\mathrm {rad} }{s}}}$	${\displaystyle 1,854858\cdot 10^{43}{\frac {\mathrm {rad} }{s}}}$
Accelerazione angolare di Planck	Accelerazione angolare ${\displaystyle \left[T\right]^{-2}}$	${\displaystyle {\frac {\omega _{\text{P}}}{t_{\text{P}}}}=t_{\text{P}}^{-2}={\frac {c^{5}}{4\pi \hbar G}}}$	${\displaystyle {\frac {\omega _{\text{P}}}{t_{\text{P}}}}=t_{\text{P}}^{-2}={\frac {c^{5}}{\hbar G}}}$	${\displaystyle 2,737862\cdot 10^{85}\;{\frac {\mathrm {rad} }{s^{2}}}}$	${\displaystyle 3,440498\cdot 10^{86}\;{\frac {\mathrm {rad} }{s^{2}}}}$
Accelerazione di Planck	Accelerazione ${\displaystyle \left[L\right]\left[T\right]^{-2}}$	${\displaystyle a_{\text{P}}={\frac {v_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{7}}{4\pi \hbar G}}}}$	${\displaystyle a_{\text{P}}={\frac {c}{t_{\text{P}}}}={\sqrt {\frac {c^{7}}{\hbar G}}}}$	${\displaystyle 1,568652\cdot 10^{51}\;{\frac {m}{s^{2}}}}$	${\displaystyle 5,560726\cdot 10^{51}\;{\frac {m}{s^{2}}}}$
Momento inerziale di Planck	Momento di inerzia ${\displaystyle \left[L\right]^{2}\left[M\right]}$	${\displaystyle m_{\text{P}}l_{\text{P}}^{2}={\sqrt {\frac {4\pi \hbar ^{3}G}{c^{5}}}}}$	${\displaystyle m_{\text{P}}l_{\text{P}}^{2}={\sqrt {\frac {\hbar ^{3}G}{c^{5}}}}}$	${\displaystyle 2,01544\cdot 10^{-77}kg\cdot m^{2}}$	${\displaystyle 5,68546\cdot 10^{-78}kg\cdot m^{2}}$
Momento angolare di Planck	Momento angolare ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-1}}$	${\displaystyle \hbar _{\text{P}}=m_{\text{P}}l_{\text{P}}^{2}\omega _{\text{P}}=l_{\text{P}}m_{\text{P}}c=E_{\text{P}}t_{\text{P}}=\hbar }$		${\displaystyle 1.054571817\ldots \cdot 10^{-34}\;\mathrm {J} s}$
Coppia di Planck	Torque ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-2}}$	${\displaystyle \tau _{\text{P}}=F_{\text{P}}l_{\text{P}}={\frac {\hbar _{P}}{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{4\pi G}}}}$	${\displaystyle \tau _{\text{P}}=F_{\text{P}}l_{\text{P}}={\frac {\hbar _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{G}}}}$	${\displaystyle 5,518004\cdot 10^{8}\mathrm {N} \cdot m}$	${\displaystyle 1,956081\cdot 10^{9}\mathrm {N} \cdot m}$
Pressione di Planck	Pressione ${\displaystyle \left[M\right]\left[L\right]^{-1}\left[T\right]^{-2}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{7}}{\hbar G^{2}}}\;}$	${\displaystyle 2,933848\cdot 10^{111}\mathrm {Pa} }$	${\displaystyle 4,632947\cdot 10^{113}\mathrm {Pa} }$
Tensione superficiale di Planck	Tensione superficiale ${\displaystyle \left[M\right]\left[T\right]^{-2}}$	${\displaystyle {\frac {F_{\text{P}}}{l_{\text{P}}}}={\sqrt {\frac {c^{11}}{64\pi ^{3}\hbar G^{3}}}}}$	${\displaystyle {\frac {F_{\text{P}}}{l_{\text{P}}}}={\sqrt {\frac {c^{11}}{\hbar G^{3}}}}}$	${\displaystyle 1,680941\cdot 10^{77}{\frac {\mathrm {N} }{m}}}$	${\displaystyle 7,488024\cdot 10^{78}{\frac {\mathrm {N} }{m}}}$
Forza superficiale universale di Planck	Forza superficiale universale ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-2}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{7}}{\hbar G^{2}}}}$	${\displaystyle 2,933848\cdot 10^{111}\mathrm {Pa} }$	${\displaystyle 4,632947\cdot 10^{113}\mathrm {Pa} }$
Durezza di indentazione di Planck	Durezza di indentazione ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-2}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{7}}{\hbar G^{2}}}}$	${\displaystyle 2,933848\cdot 10^{111}\mathrm {Pa} }$	${\displaystyle 4,632947\cdot 10^{113}\mathrm {Pa} }$
Durezza assoluta di Planck	Durezza Assoluta ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-2}}$	${\displaystyle {\frac {a_{\oplus }}{F_{\text{P}}}}={\frac {_{9,80665}\,4\pi G}{c^{4}}}}$	${\displaystyle {\frac {a_{\oplus }}{F_{\text{P}}}}={\frac {_{9,80665}G}{c^{4}}}}$	${\displaystyle 1,01825\cdot 10^{-42}kg\cdot f}$	${\displaystyle 8,10296\cdot 10^{-44}kg\cdot f}$
Flusso di massa di Planck	Rapporto di flusso di massa ${\displaystyle \left[M\right]\left[T\right]^{-1}}$	${\displaystyle {t_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{t_{\text{P}}}}={\frac {c}{2\pi r_{s}}}={\frac {c^{3}}{4\pi G}}}$	${\displaystyle {t_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{t_{\text{P}}}}={\frac {2c}{r_{s}}}={\frac {c^{3}}{G}}}$	${\displaystyle 3,212525\cdot 10^{34}\;{\frac {kg}{s}}}$	${\displaystyle 4,036978\cdot 10^{35}\;{\frac {kg}{s}}}$
Viscosità di Planck	viscosità dinamica ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-1}}$	${\displaystyle \eta _{\text{P}}=P_{\text{P}}t_{\text{P}}={\sqrt {\frac {c^{9}}{64\pi ^{3}\hbar G^{3}}}}}$	${\displaystyle \eta _{\text{P}}=P_{\text{P}}t_{\text{P}}={\sqrt {\frac {c^{9}}{\hbar G^{3}}}}}$	${\displaystyle 5,607015\cdot 10^{68}\mathrm {Pa} \cdot s}$	${\displaystyle 2,497736\cdot 10^{70}\mathrm {Pa} \cdot s}$
Viscosità cinematica di Planck	viscosità cinematica ${\displaystyle \left[L\right]^{2}\left[T\right]^{-1}}$	${\displaystyle {\frac {\eta _{\text{P}}}{\rho _{\text{P}}}}={\frac {l_{\text{P}}^{2}}{t_{\text{P}}}}={\sqrt {\frac {4\pi \hbar G}{c}}}}$	${\displaystyle {\frac {\eta _{\text{P}}}{\rho _{\text{P}}}}={\frac {l_{\text{P}}^{2}}{t_{\text{P}}}}={\sqrt {\frac {\hbar G}{c}}}}$	${\displaystyle 1,717653\cdot 10^{-27}{\frac {m^{2}}{s}}}$	${\displaystyle 4,845411\cdot 10^{-27}{\frac {m^{2}}{s}}}$
Portata volumetrica di Planck	Rapporto di flusso volumetrico ${\displaystyle \left[L\right]^{3}\left[T\right]^{-1}}$	${\displaystyle Q_{\text{P}}={\frac {l_{\text{P}}^{3}}{t_{\text{P}}}}=l_{\text{P}}^{2}v_{\text{P}}={\frac {4\pi \hbar G}{c^{2}}}}$	${\displaystyle Q_{\text{P}}={\frac {l_{\text{P}}^{3}}{t_{\text{P}}}}=l_{\text{P}}^{2}v_{\text{P}}={\frac {\hbar \,G}{c^{2}}}}$	${\displaystyle 9,841252\cdot 10^{-61}\;{\frac {m^{3}}{s}}}$	${\displaystyle 7,831419\cdot 10^{-62}\;{\frac {m^{3}}{s}}}$
Proprietà elettromagnetiche
Corrente di Planck	Corrente elettrica ${\displaystyle \left[Q\right]\left[T\right]^{-1}}$	${\displaystyle I_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {\varepsilon _{0}c^{6}}{4\pi G}}}}$	${\displaystyle I_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{6}}{G}}}}$	${\displaystyle 2,768399\cdot 10^{24}\;\mathrm {A} }$	${\displaystyle 3,478873\cdot 10^{25}\;\mathrm {A} }$
Forza magnetomotiva di Planck	Corrente elettrica ${\displaystyle \left[Q\right]\left[T\right]^{-1}}$	${\displaystyle I_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {\varepsilon _{0}c^{6}}{4\pi G}}}}$	${\displaystyle I_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{6}}{G}}}}$	${\displaystyle 2,768399\cdot 10^{24}\;\mathrm {A} }$	${\displaystyle 3,478873\cdot 10^{25}\;\mathrm {A} }$
Tensione di Planck	Tensione ${\displaystyle \left[M\right]\left[L\right]^{2}\left[T\right]^{-2}\left[Q\right]^{-1}}$	${\displaystyle V_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi \varepsilon _{0}G}}}}$		${\displaystyle 1,042940\cdot 10^{27}\;\mathrm {V} }$
Forza elettromotiva di Planck	Tensione ${\displaystyle \left[M\right]\left[L\right]^{2}\left[T\right]^{-2}\left[Q\right]^{-1}}$	${\displaystyle \phi _{\text{P}}=V_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi \varepsilon _{0}G}}}}$		${\displaystyle 1.042\;940\cdot 10^{27}\;\mathrm {V} }$
Resistenza di Planck	Resistenza elettrica ${\displaystyle \left[M\right]\left[L\right]^{2}\left[T\right]^{-1}\left[Q\right]^{-2}}$	${\displaystyle Z_{\text{P}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{\varepsilon _{0}c}}=\mu _{0}c=Z_{0}}$	${\displaystyle Z_{\text{P}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {1}{4\pi \varepsilon _{0}c}}={\frac {Z_{0}}{4\pi }}}$	${\displaystyle 376,730\;\Omega }$	${\displaystyle 29,9792458\;\Omega }$
Conduttanza di Planck	Conduttanza elettrica ${\displaystyle \left[L\right]^{-2}\left[M\right]^{-1}\left[T\right]\left[Q\right]^{2}}$	${\displaystyle G_{\text{P}}={\frac {1}{R_{\text{P}}}}=\varepsilon _{0}c={\frac {1}{Z_{0}}}}$	${\displaystyle G_{\text{P}}={\frac {1}{R_{\text{P}}}}=4\pi \varepsilon _{0}c={\frac {4\pi }{Z_{0}}}}$	${\displaystyle 0,002654\;\mathrm {S} }$	${\displaystyle 0,0333564095\;\mathrm {S} }$
Capacità elettrica di Planck	Capacità elettrica ${\displaystyle \left[L\right]^{-2}\left[M\right]^{-1}\left[T\right]^{2}\left[Q\right]^{2}}$	${\displaystyle {{C}_{\text{P}}}={\frac {{q}_{\text{P}}}{{V}_{\text{P}}}}={\frac {{l}_{P}}{{k}_{e}}}={\sqrt {\frac {4{\pi }\varepsilon _{0}^{2}\hbar G}{{c}^{3}}}}}$	${\displaystyle {{C}_{\text{P}}}={\frac {{q}_{\text{P}}}{{V}_{\text{P}}}}={\frac {{l}_{P}}{{k}_{e}}}={\sqrt {\frac {16{{\pi }^{2}}\varepsilon _{0}^{2}\hbar G}{{c}^{3}}}}}$	${\displaystyle 5,072985\cdot 10^{-46}\;\mathrm {F} }$	${\displaystyle 1,798326\cdot 10^{-45}\;\mathrm {F} }$
Permittività di Planck (Costante elettrica)	Permittività elettrica ${\displaystyle \left[L\right]^{-3}\left[M\right]^{-1}\left[T\right]^{2}\left[Q\right]^{2}}$	${\displaystyle \varepsilon _{\text{P}}={\frac {C_{\text{P}}}{l_{\text{P}}}}={\frac {q_{\text{P}}}{V_{\text{P}}l_{\text{P}}}}={\frac {F_{\text{P}}}{V_{\text{P}}^{2}}}=\varepsilon _{0}}$	${\displaystyle \varepsilon _{\text{P}}={\frac {C_{\text{P}}}{l_{\text{P}}}}={\frac {F_{\text{P}}}{V_{\text{P}}^{2}}}={\frac {1}{k_{\text{e}}}}=4\pi \varepsilon _{0}}$	${\displaystyle 8,854187813\cdot 10^{-12}{\frac {\mathrm {F} }{m}}}$	${\displaystyle 1,11265006\cdot 10^{-10}{\frac {\mathrm {F} }{m}}}$
Permeabilità di Planck (Costante magnetica)	Permeabilità magnetica ${\displaystyle \left[L\right]\left[M\right]\left[Q\right]^{-2}}$	${\displaystyle \mu _{\text{P}}={\frac {L_{\text{P}}}{l_{\text{P}}}}={\frac {{\phi }_{\text{P}}^{B}}{l_{\text{P}}}}={\frac {1}{\varepsilon _{0}c^{2}}}=\mu _{0}}$	${\displaystyle \mu _{\text{P}}={\frac {L_{\text{P}}}{l_{\text{P}}}}={\frac {V_{\text{P}}}{{I_{m}}_{\text{P}}}}={\frac {1}{4\pi \,\varepsilon _{0}c^{2}}}={\frac {\mu _{0}}{4\pi }}}$	${\displaystyle 1,25663706212{\frac {\mathrm {\mu H} }{m}}}$	${\displaystyle 10,0000000055{\frac {\mathrm {\mu H} }{m}}}$
Induttanza elettrica di Planck	Induttanza ${\displaystyle \left[L\right]^{2}\left[M\right]\left[Q\right]^{-2}}$	${\displaystyle L_{\text{P}}={\frac {E_{\text{P}}}{I_{\text{P}}}}={\frac {m_{\text{P}}l_{\text{P}}^{2}}{q_{\text{P}}^{2}}}={\sqrt {\frac {4\pi \hbar G}{\varepsilon _{0}^{2}c^{7}}}}}$	${\displaystyle L_{\text{P}}={\frac {E_{\text{P}}}{I_{\text{P}}^{2}}}={\frac {m_{\text{P}}l_{\text{P}}^{2}}{q_{\text{P}}^{2}}}={\sqrt {\frac {G\hbar }{16\pi ^{2}\varepsilon _{0}^{2}c^{7}}}}}$	${\displaystyle 7,199871\cdot 10^{-41}\mathrm {H} }$	${\displaystyle 1,61625518\cdot 10^{-42}\mathrm {H} }$
Resistività elettrica di Planck	Resistività elettrica ${\displaystyle \left[L\right]^{3}\left[M\right]\left[T\right]^{-1}\left[Q\right]^{-2}}$	${\displaystyle Z_{\text{P}}^{\rho }=Z_{\text{P}}l_{\text{P}}=t_{\text{P}}k_{\text{e}}={\sqrt {\frac {4\pi \hbar G}{\varepsilon _{0}^{2}c^{5}}}}}$	${\displaystyle Z_{\text{P}}^{\rho }=Z_{\text{P}}l_{\text{P}}=t_{\text{P}}k_{\text{e}}={\sqrt {\frac {\hbar G}{16\pi ^{2}\varepsilon _{0}^{2}c^{5}}}}}$	${\displaystyle 2,15847\cdot 10^{-32}\Omega \cdot m}$	${\displaystyle 4,84541\cdot 10^{-34}\Omega \cdot m}$
Conduttività elettrica di Planck	Conduttività elettrica ${\displaystyle \left[L\right]^{-3}\left[M\right]^{-1}\left[T\right]\left[Q\right]^{2}}$	${\displaystyle \sigma _{\text{P}}={\frac {1}{Z_{\text{P}}^{\rho }}}={\sqrt {\frac {\varepsilon _{0}^{2}c^{5}}{4\pi \hbar G}}}}$	${\displaystyle \sigma _{\text{P}}={\frac {1}{Z_{\text{P}}^{\rho }}}={\sqrt {\frac {16\pi ^{2}\varepsilon _{0}^{2}c^{5}}{\hbar G}}}}$	${\displaystyle 4,632918\cdot 10^{31}{\frac {\mathrm {S} }{m}}}$	${\displaystyle 2,063809\cdot 10^{33}{\frac {\mathrm {S} }{m}}}$
Densità di carica di Planck	Densità di carica ${\displaystyle \left[L\right]^{-3}\left[Q\right]}$	${\displaystyle {\rho _{e}}_{\text{P}}={\frac {q_{\text{P}}}{l_{\text{P}}^{3}}}={\sqrt {\frac {\varepsilon _{0}c^{10}}{64\pi ^{3}\hbar ^{2}G^{3}}}}}$	${\displaystyle {\rho _{e}}_{\text{P}}={\frac {q_{\text{P}}}{l_{\text{P}}^{3}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{10}}{\hbar ^{2}G^{3}}}}}$	${\displaystyle 2,813056\cdot 10^{86}{\frac {\mathrm {C} }{m^{3}}}}$	${\displaystyle 4,442200\cdot 10^{86}{\frac {\mathrm {C} }{m^{3}}}}$
Forza del campo elettrico di Planck	Campo elettrico ${\displaystyle \left[L\right]\left[M\right]\left[T\right]^{-2}\left[Q\right]^{-1}}$	${\displaystyle {\bf {E}}_{\text{P}}={\frac {F_{\text{P}}}{q_{\text{P}}}}={\sqrt {\frac {c^{7}}{16\pi ^{2}\varepsilon _{0}\hbar G^{2}}}}}$	${\displaystyle {\bf {E}}_{\text{P}}={\frac {F_{\text{P}}}{q_{\text{P}}}}={\sqrt {\frac {c^{7}}{4\pi \varepsilon _{0}\hbar G^{2}}}}}$	${\displaystyle 1,820306\cdot 10^{61}{\frac {\mathrm {V} }{m}}}$	${\displaystyle 6,452817\cdot 10^{61}{\frac {\mathrm {V} }{m}}}$
Forza del campo magnetico di Planck	Campo magnetico ${\displaystyle \left[L\right]^{-1}\left[T\right]^{-1}\left[Q\right]}$	${\displaystyle {\bf {H}}_{\text{P}}={\frac {I_{\text{P}}}{l_{\text{P}}}}={\sqrt {\frac {\varepsilon _{0}c^{9}}{16\pi ^{2}\hbar G^{2}}}}}$	${\displaystyle {\bf {H}}_{\text{P}}={\frac {I_{\text{P}}}{l_{\text{P}}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{9}}{\hbar G^{2}}}}}$	${\displaystyle 4,831855\cdot 10^{58}{\frac {\mathrm {A} }{m}}}$	${\displaystyle 2,152428\cdot 10^{60}{\frac {\mathrm {A} }{m}}}$
Induzione elettrica di Planck	Corrente di spostamento ${\displaystyle \left[L\right]^{-2}\left[T\right]^{-1}\left[Q\right]}$	${\displaystyle {\bf {D}}_{\text{P}}={\frac {q_{\text{P}}}{l_{\text{P}}^{2}}}={\sqrt {\frac {\varepsilon _{0}c^{7}}{16\pi ^{2}\hbar G^{2}}}}}$	${\displaystyle {\bf {D}}_{\text{P}}={\frac {q_{\text{P}}}{l_{\text{P}}^{2}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{7}}{\hbar G^{2}}}}}$	${\displaystyle 1,611733\cdot 10^{50}{\frac {\mathrm {C} }{m^{2}}}}$	${\displaystyle 7,179727\cdot 10^{51}{\frac {\mathrm {C} }{m^{2}}}}$
Induzione magnetica di Planck	Campo magnetico ${\displaystyle \left[M\right]\left[T\right]^{-1}\left[Q\right]^{-1}}$	${\displaystyle {\bf {B}}_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}I_{\text{P}}}}={\sqrt {\frac {c^{5}}{16\pi ^{2}\varepsilon _{0}\hbar G^{2}}}}}$	${\displaystyle {\bf {B}}_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}I_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}l_{\text{P}}^{2}}}={\sqrt {\frac {c^{5}}{4\pi \varepsilon _{0}\hbar G^{2}}}}}$	${\displaystyle 6,071888\cdot 10^{52}\;\mathrm {T} }$	${\displaystyle 2,152428\cdot 10^{53}\;\mathrm {T} }$
Flusso elettrico di Planck	Flusso magnetico ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-1}\left[Q\right]^{-1}}$	${\displaystyle {\phi }_{\text{P}}^{E}={\bf {E}}_{\text{P}}l_{\text{P}}^{2}=\phi _{\text{P}}l_{\text{P}}={\sqrt {\frac {\hbar c}{\varepsilon _{0}}}}}$	${\displaystyle {\phi }_{\text{P}}^{E}={\bf {E}}_{\text{P}}l_{\text{P}}^{2}=\phi _{\text{P}}l_{\text{P}}={\sqrt {\frac {\hbar c}{4\pi \varepsilon _{0}}}}}$	${\displaystyle 5,975498\cdot 10^{-8}\mathrm {V} \cdot m}$	${\displaystyle 1,685657\cdot 10^{-8}\mathrm {V} \cdot m}$
Flusso magnetico di Planck	Flusso magnetico ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-1}\left[Q\right]^{-1}}$	${\displaystyle {\phi }_{\text{P}}^{B}={\bf {B}}_{\text{P}}l_{\text{P}}^{2}={\bf {A}}_{\text{P}}l_{\text{P}}={\sqrt {\frac {\hbar }{\varepsilon _{0}c}}}}$	${\displaystyle {\phi }_{\text{P}}^{B}={\frac {E_{\text{P}}}{I_{\text{P}}}}={\bf {A}}_{\text{P}}l_{\text{P}}={\frac {\hbar }{q_{\text{P}}}}={\sqrt {\frac {\hbar }{4\pi \varepsilon _{0}c}}}}$	${\displaystyle 1,993211\cdot 10^{-16}\,\mathrm {Wb} }$	${\displaystyle 5,622746\cdot 10^{-17}\;\mathrm {Wb} }$
Potenziale elettrico di Planck	Tensione ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-2}\left[Q\right]^{-1}}$	${\displaystyle \phi _{\text{P}}=V_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi \varepsilon _{0}G}}}}$		${\displaystyle 1,042940\cdot 10^{27}\;\mathrm {V} }$
Potenziale magnetico di Planck	Corrente magnetica ${\displaystyle \left[L\right]\left[M\right]\left[T\right]^{-1}\left[Q\right]^{-1}}$	${\displaystyle {{\bf {A}}_{\text{P}}}={\frac {{E}_{\text{P}}}{{{q}_{m}}_{\text{P}}}}={\frac {{F}_{\text{P}}}{{I}_{\text{P}}}}={\frac {{V}_{\text{P}}}{{v}_{\text{P}}}}={{\bf {B}}_{\text{P}}}{{l}_{\text{P}}}={\frac {\hbar }{{{q}_{\text{P}}}{{l}_{\text{P}}}}}={\sqrt {\frac {{c}^{2}}{4\pi {{\varepsilon }_{0}}G}}}}$		${\displaystyle 3,478873\cdot 10^{18}\;\mathrm {T} \cdot m}$
Densità di corrente di Planck	Densità di corrente elettrica ${\displaystyle \left[L\right]^{-2}\left[T\right]^{-1}\left[Q\right]}$	${\displaystyle {\bf {J}}_{\text{P}}={\frac {I_{\text{P}}}{l_{\text{P}}^{2}}}={{\rho }_{e}}_{\text{P}}v_{\text{P}}={\sqrt {\frac {\varepsilon _{0}c^{12}}{64\pi ^{3}\hbar ^{2}G^{3}}}}}$	${\displaystyle {\bf {J}}_{\text{P}}={\frac {I_{\text{P}}}{l_{\text{P}}^{2}}}={{\rho }_{e}}_{\text{P}}v_{\text{P}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{12}}{\hbar ^{2}G^{3}}}}}$	${\displaystyle 8,433329\cdot 10^{92}\;{\frac {\mathrm {A} }{m^{2}}}}$	${\displaystyle 1,331738\cdot 10^{95}\;{\frac {\mathrm {A} }{m^{2}}}}$
Momento elettrico di Planck	Dipolo elettrico ${\displaystyle \left[L\right]\left[Q\right]}$	${\displaystyle {d}_{\text{P}}=q_{\text{P}}l_{\text{P}}={\sqrt {\frac {4\pi \varepsilon _{0}\hbar ^{2}G}{c^{2}}}}}$		${\displaystyle 3,031361\cdot 10^{-53}\;\mathrm {C} \cdot m}$
Momento magnetico di Planck	Dipolo magnetico ${\displaystyle \left[L\right]^{2}\left[T\right]^{-1}\left[Q\right]}$	${\displaystyle {\mu _{d}}_{\text{P}}={q_{m}}_{\text{P}}l_{\text{P}}=I_{\text{P}}l_{\text{P}}^{2}={\sqrt {4\pi \varepsilon _{0}\hbar ^{2}G}}}$		${\displaystyle 9,087791\cdot 10^{-45}\;{\frac {\mathrm {J} }{\mathrm {T} }}}$
Monopolo magnetico di Planck	Carica magnetica ${\displaystyle \left[L\right]\left[T\right]^{-1}\left[Q\right]}$	${\displaystyle {{q}_{m}}_{\text{P}}=q_{\text{P}}v_{P}={\frac {F_{\text{P}}}{{\bf {B}}_{\text{P}}}}={\sqrt {{{\varepsilon }_{0}}\hbar {{c}^{3}}}}}$	${\displaystyle {{q}_{m}}_{\text{P}}=q_{\text{P}}v_{P}={\frac {4\pi }{\mu _{0}}}\phi _{\text{P}}^{B}={\sqrt {4\pi {{\varepsilon }_{0}}\hbar {{c}^{3}}}}}$	${\displaystyle 1.586147\cdot 10^{-10}{\frac {\mathrm {N} }{\mathrm {T} }}}$	${\displaystyle 5.622746\cdot 10^{-10}\mathrm {A} \cdot m}$
Corrente magnetica di Planck	Corrente magnetica ${\displaystyle \left[L\right]\left[T\right]^{-2}\left[Q\right]}$	${\displaystyle {I_{m}}_{\text{P}}={\frac {{q_{m}}_{\text{P}}}{t_{\text{P}}}}={q_{\text{P}}}{a_{\text{P}}}={I_{\text{P}}}{v_{\text{P}}}={\sqrt {\frac {\varepsilon _{0}c^{8}}{4\pi G}}}}$	${\displaystyle {I_{m}}_{\text{P}}={\frac {{q_{m}}_{\text{P}}}{t_{\text{P}}}}={q_{\text{P}}}{a_{\text{P}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{8}}{G}}}}$	${\displaystyle 8,29945\cdot 10^{32}{\frac {\mathrm {V} \cdot m}{\mathrm {H} }}}$	${\displaystyle 1,04294\cdot 10^{34}{\frac {\mathrm {W} }{\mathrm {T} \cdot m}}}$
Densità di corrente magnetica di Planck	Corrente magnetica ${\displaystyle \left[L\right]^{-1}\left[T\right]^{-2}\left[Q\right]}$	${\displaystyle {\frac {{I_{m}}_{\text{P}}}{l_{\text{P}}^{2}}}={\bf {J}}_{\text{P}}v_{\text{P}}={\frac {{I}_{\text{P}}}{l_{\text{P}}t_{\text{P}}}}={\sqrt {\frac {\varepsilon _{0}c^{14}}{64\pi ^{3}\hbar ^{2}G^{3}}}}}$	${\displaystyle {\frac {{I_{m}}_{\text{P}}}{l_{\text{P}}^{2}}}={\bf {J}}_{\text{P}}v_{\text{P}}={\frac {{I}_{\text{P}}}{l_{\text{P}}t_{\text{P}}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{14}}{\hbar ^{2}G^{3}}}}}$	${\displaystyle 2,52825\cdot 10^{101}{\frac {\mathrm {V} }{m\cdot \mathrm {H} }}}$	${\displaystyle 3,99245\cdot 10^{103}{\frac {\mathrm {V} }{m\cdot \mathrm {H} }}}$
Carica specifica di Planck	carica specifica ${\displaystyle \left[M\right]^{-1}\left[Q\right]}$	${\displaystyle q_{r_{\text{s}}}={\frac {q_{\text{P}}}{m_{\text{P}}}}={\sqrt {\frac {2\pi {r_{\text{s}}}}{\mu _{0}}}}={\sqrt {\frac {G}{k_{e}}}}={\sqrt {4\pi \varepsilon _{0}G}}}$		${\displaystyle 8.617517\cdot 10^{-11}\;{\frac {\mathrm {Hz} }{\mathrm {T} }}}$
Monopolo specifica di Planck[non chiaro]	carica magnetica specifica ${\displaystyle \left[L\right]\left[T\right]^{-1}\left[M\right]^{-1}\left[Q\right]}$	${\displaystyle q_{r_{\text{s}}}c={\frac {q_{\text{P}}c}{m_{\text{P}}}}={\frac {a_{\text{P}}}{{\bf {B}}_{\text{P}}}}={\sqrt {4\pi \varepsilon _{0}c^{2}G}}}$	${\displaystyle q_{r_{\text{s}}}c={\frac {q_{\text{P}}c}{m_{\text{P}}}}={\frac {a_{\text{P}}}{{\bf {B}}_{\text{P}}}}={\sqrt {\frac {4\pi G}{\mu _{0}}}}}$	${\displaystyle 0,0258347{\frac {m}{s^{2}\cdot \mathrm {T} }}}$	${\displaystyle 0,0258347{\frac {m}{s^{2}\cdot \mathrm {T} }}}$
Proprietà termodinamiche
Temperatura di Planck in 2π	Temperatura ${\displaystyle \left[\Theta \right]}$	${\displaystyle {\Theta }_{\text{P}}^{_{2\pi }}=2\pi {\Theta _{\text{P}}}={\frac {2\pi E_{\text{P}}}{k_{\text{B}}}}={\sqrt {\frac {\pi \hbar c^{5}}{G{k_{\text{B}}^{2}}}}}}$	${\displaystyle \Theta _{\text{P}}^{_{2\pi }}=2\pi {\Theta _{\text{P}}}={\frac {2\pi m_{\text{P}}c^{2}}{k_{\text{B}}}}={\sqrt {\frac {\pi \hbar c^{5}}{Gk_{\text{B}}^{2}}}}}$	${\displaystyle 2,511185\cdot 10^{32}\mathrm {K} }$	${\displaystyle 8,901917\cdot 10^{32}\mathrm {K} }$
Entropia di Planck	Entropia ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-2}\left[\Theta \right]^{-1}}$	${\displaystyle S_{\text{P}}={\frac {E_{\text{P}}}{\Theta _{\text{P}}}}=k_{\text{B}}}$		${\displaystyle 1,380649\cdot 10^{-23}{\frac {\mathrm {J} }{\mathrm {K} }}}$
Entropia di Planck in 2 π	Entropia ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-2}\left[\Theta \right]^{-1}}$	${\displaystyle {S_{2\pi }}_{\text{P}}={\frac {E_{\text{P}}}{2\pi \Theta _{\text{P}}}}={\frac {k_{\text{B}}}{2\pi }}}$		${\displaystyle 2,197371\cdot 10^{-24}{\frac {\mathrm {J} }{\mathrm {K} }}}$
Coefficiente di dilatazione termica di Planck	Coefficiente di dilatazione termica ${\displaystyle \left[\Theta \right]^{-1}}$	${\displaystyle {\alpha _{_{V}}}_{\text{P}}={\frac {1}{\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{E_{\text{P}}}}={\sqrt {\frac {4\pi G{k_{\text{B}}}^{2}}{\hbar c^{5}}}}}$	${\displaystyle {\alpha _{_{V}}}_{\text{P}}={\frac {1}{\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{E_{\text{P}}}}={\sqrt {\frac {G{k_{\text{B}}}^{2}}{\hbar c^{5}}}}}$	${\displaystyle 2,502080\cdot 10^{-33}{\frac {1}{\mathrm {K} }}}$	${\displaystyle 7,058238\cdot 10^{-33}{\frac {1}{\mathrm {K} }}}$
Capacità termica di Planck	Capacità termica - Entropia ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-2}\left[\Theta \right]^{-1}}$	${\displaystyle {C}_{\text{P}}^{\Theta }={\frac {E_{\text{P}}}{\Theta _{\text{P}}}}=k_{\text{B}}}$		${\displaystyle 1,380649\cdot 10^{-23}{\frac {\mathrm {J} }{\mathrm {K} }}}$
Calore specifico di Planck	Calore specifico ${\displaystyle \left[L\right]^{2}\left[T\right]^{-2}\left[\Theta \right]^{-1}}$	${\displaystyle {c_{p}}_{\text{P}}={\frac {E_{\text{P}}}{m_{\text{P}}\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{m_{\text{P}}}}={\sqrt {\frac {4\pi Gk_{\text{B}}^{2}}{\hbar c}}}}$	${\displaystyle {c_{p}}_{\text{P}}={\frac {E_{\text{P}}}{m_{\text{P}}\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{m_{\text{P}}}}={\sqrt {\frac {Gk_{\text{B}}^{2}}{\hbar c}}}}$	${\displaystyle 2,24876\cdot 10^{-15}{\frac {\mathrm {J} }{kg\cdot \mathrm {K} }}}$	${\displaystyle 6,34363\cdot 10^{-16}{\frac {\mathrm {J} }{kg\cdot \mathrm {K} }}}$
Calore volumetrico di Planck	Calore volumetrico ${\displaystyle \left[L\right]^{-1}\left[M\right]\left[T\right]^{-2}\left[\Theta \right]^{-1}}$	${\displaystyle {c_{V}}_{\text{P}}={\frac {E_{\text{P}}}{l_{\text{P}}^{3}\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{l_{\text{P}}^{3}}}={\sqrt {\frac {c^{9}k_{\text{B}}^{2}}{64\pi ^{3}\hbar ^{3}G^{3}}}}}$	${\displaystyle {c_{V}}_{\text{P}}={\frac {E_{\text{P}}}{l_{\text{P}}^{3}\Theta _{\text{P}}}}={\frac {k_{\text{B}}}{l_{\text{P}}^{3}}}={\sqrt {\frac {c^{9}k_{\text{B}}^{2}}{\hbar ^{3}G^{3}}}}}$	${\displaystyle 7,340723\cdot 10^{79}{\frac {\mathrm {J} }{m^{3}\cdot \mathrm {K} }}}$	${\displaystyle 3,270044\cdot 10^{81}{\frac {\mathrm {J} }{m^{3}\cdot \mathrm {K} }}}$
Resistenza termica di Planck	Resistenza termica ${\displaystyle \left[L\right]^{-2}\left[M\right]^{-1}\left[T\right]^{3}\left[\Theta \right]}$	${\displaystyle {\Omega _{\Theta }}_{\text{P}}={\frac {\Theta _{\text{P}}}{P_{\text{P}}}}={\frac {t_{\text{P}}}{k_{\text{B}}}}={\sqrt {\frac {4\pi \hbar G}{c^{5}k_{\text{B}}^{2}}}}}$	${\displaystyle {\Omega _{\Theta }}_{\text{P}}={\frac {\Theta _{\text{P}}}{P_{\text{P}}}}={\frac {t_{\text{P}}}{k_{\text{B}}}}={\sqrt {\frac {\hbar G}{c^{5}k_{\text{B}}^{2}}}}}$	${\displaystyle 1,384238\cdot 10^{-20}{\frac {\mathrm {K} }{\mathrm {W} }}}$	${\displaystyle 3,904864\cdot 10^{-21}{\frac {\mathrm {K} }{\mathrm {W} }}}$
Conduttanza termica di Planck	Conduttanza termica ${\displaystyle \left[L\right]^{2}\left[M\right]\left[T\right]^{-3}\left[\Theta \right]^{-1}}$	${\displaystyle {G_{\Theta }}_{\text{P}}={\frac {k_{\text{B}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}k_{\text{B}}^{2}}{4\pi \hbar G}}}\simeq {\bf {A}}_{\text{P}}{\frac {2\pi }{\sqrt {\alpha }}}}$	${\displaystyle {G_{\Theta }}_{\text{P}}={\frac {1}{{\Omega _{\Theta }}_{\text{P}}}}={\frac {k_{\text{B}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}k_{\text{B}}^{2}}{\hbar G}}}}$	${\displaystyle 7,224190\cdot 10^{19}{\frac {\mathrm {W} }{\mathrm {K} }}}$	${\displaystyle 2,560909\cdot 10^{20}{\frac {\mathrm {W} }{\mathrm {K} }}}$
Resistività termica di Planck	Resistività termica ${\displaystyle \left[L\right]^{-1}\left[M\right]^{-1}\left[T\right]^{3}\left[\Theta \right]}$	${\displaystyle {\frac {1}{{\lambda _{\Theta }}_{\text{P}}}}={\Omega _{\Theta }}_{\text{P}}l_{\text{P}}={\frac {l_{\text{P}}t_{\text{P}}}{k_{\text{B}}}}={\sqrt {\frac {16\pi ^{2}\hbar ^{2}G^{2}}{c^{8}k_{\text{B}}^{2}}}}}$	${\displaystyle {\frac {1}{{\lambda _{\Theta }}_{\text{P}}}}={\Omega _{\Theta }}_{\text{P}}\,l_{\text{P}}={\frac {l_{\text{P}}t_{\text{P}}}{k_{\text{B}}}}={\sqrt {\frac {\hbar ^{2}G^{2}}{c^{8}k_{\text{B}}^{2}}}}}$	${\displaystyle 7,930958\cdot 10^{-55}{\frac {m\cdot \mathrm {K} }{\mathrm {W} }}}$	${\displaystyle 6,311256\cdot 10^{-56}{\frac {m\cdot \mathrm {K} }{\mathrm {W} }}}$
Conducibilità termica di Planck	Conducibilità termica ${\displaystyle \left[L\right]\left[M\right]\left[T\right]^{-3}\left[\Theta \right]^{-1}}$	${\displaystyle {\lambda _{\Theta }}_{\text{P}}={\frac {P_{\text{P}}}{l_{\text{P}}\Theta _{\text{P}}}}={\sqrt {\frac {c^{8}k_{\text{B}}^{2}}{16\pi ^{2}\hbar ^{2}G^{2}}}}\simeq {\bf {B}}_{\text{P}}{\frac {2\pi }{\sqrt {\alpha }}}}$	${\displaystyle {\lambda _{\Theta }}_{\text{P}}={\frac {P_{\text{P}}}{l_{\text{P}}\Theta _{\text{P}}}}={\sqrt {\frac {c^{8}k_{\text{B}}^{2}}{\hbar ^{2}G^{2}}}}\simeq {\bf {B}}_{\text{P}}{\frac {2\pi }{\sqrt {\alpha }}}}$	${\displaystyle 1,260881\cdot 10^{54}{\frac {\mathrm {W} }{m\cdot \mathrm {K} }}}$	${\displaystyle 1,584471\cdot 10^{55}{\frac {\mathrm {W} }{m\cdot \mathrm {K} }}}$
Isolatore termico di Planck	Isolatore termico ${\displaystyle \left[M\right]^{-1}\left[T\right]^{3}\left[\Theta \right]}$	${\displaystyle {\frac {l_{\text{P}}}{{\lambda _{\Theta }}_{\text{P}}}}={\Omega _{\Theta }}_{\text{P}}l_{\text{P}}^{2}={\sqrt {\frac {64\pi ^{3}\hbar ^{3}G^{3}}{c^{11}k_{\text{B}}^{2}}}}}$	${\displaystyle {\frac {l_{\text{P}}}{{\lambda _{\Theta }}_{\text{P}}}}={\Omega _{\Theta }}_{\text{P}}l_{\text{P}}^{2}={\sqrt {\frac {\hbar ^{3}G^{3}}{c^{11}k_{\text{B}}^{2}}}}}$	${\displaystyle 4,54402\cdot 10^{-89}{\frac {m^{2}\cdot \mathrm {K} }{\mathrm {W} }}}$	${\displaystyle 1,02006\cdot 10^{-90}{\frac {m^{2}\cdot \mathrm {K} }{\mathrm {W} }}}$
Trasmittanza termica di Planck	Trasmittanza termica ${\displaystyle \left[M\right]\left[T\right]^{-3}\left[\Theta \right]^{-1}}$	${\displaystyle {\frac {{\lambda _{\Theta }}_{\text{P}}}{l_{\text{P}}}}={\frac {1}{{\Omega _{\Theta }}_{\text{P}}l_{\text{P}}^{2}}}={\sqrt {\frac {c^{11}k_{\text{B}}^{2}}{64\pi ^{3}\hbar ^{3}G^{3}}}}}$	${\displaystyle {\frac {{\lambda _{\Theta }}_{\text{P}}}{l_{\text{P}}}}={\frac {1}{{\Omega _{\Theta }}_{\text{P}}l_{\text{P}}^{2}}}={\sqrt {\frac {c^{11}k_{\text{B}}^{2}}{64\pi ^{3}\hbar ^{3}G^{3}}}}}$	${\displaystyle 2,200693\cdot 10^{88}{\frac {\mathrm {W} }{m^{2}\cdot \mathrm {K} }}}$	${\displaystyle 9,803346\cdot 10^{89}{\frac {\mathrm {W} }{m^{2}\cdot \mathrm {K} }}}$
Flusso termico di Planck	Intensità luminosa ${\displaystyle \left[M\right]\left[T\right]^{-3}}$	${\displaystyle {\phi _{q}}_{\text{P}}={\lambda _{\Theta }}_{\text{P}}\Theta _{\text{P}}=i_{\text{P}}={\frac {P_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{8}}{16\pi ^{2}\hbar G^{2}}}}$	${\displaystyle {\phi _{q}}_{\text{P}}={\lambda _{\Theta }}_{\text{P}}\Theta _{\text{P}}=i_{\text{P}}={\frac {P_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{8}}{\hbar G^{2}}}}$	${\displaystyle 8,795455\cdot 10^{119}{\frac {\mathrm {W} }{m^{2}}}}$	${\displaystyle 1,388923\cdot 10^{122}{\frac {\mathrm {W} }{m^{2}}}}$
Località di Planck	Seconda radiazione di costante ${\displaystyle \left[L\right]\left[\Theta \right]}$	${\displaystyle C_{2_{\text{P}}}={\Theta _{\text{P}}l_{\text{P}}}={\frac {C_{2}}{2\pi }}={\frac {hc}{2\pi \,{k}_{\text{B}}}}={\frac {{E}_{\text{P}}{l}_{\text{P}}}{{k}_{\text{B}}}}}$		${\displaystyle 0,002289885\;\mathrm {K} \cdot m}$
Località di Planck con costante di struttura fine	Seconda radiazione di costante ${\displaystyle \left[L\right]\left[\Theta \right]}$	${\displaystyle C_{\alpha _{\text{P}}}={\frac {2\pi \Theta _{\text{P}}l_{\text{P}}}{\sqrt {\alpha }}}={\frac {C_{2}}{\sqrt {\alpha }}}={\frac {hc}{{\sqrt {\alpha }}{k}_{\text{B}}}}={\frac {2\pi {E}_{\text{P}}{l}_{\text{P}}}{{\sqrt {\alpha }}{k}_{\text{B}}}}\simeq q_{\text{P}}c^{2}}$		${\displaystyle 0,168427\;\mathrm {K} \cdot m}$
Costante di Stefan-Boltzmann di Planck	Costante di proporzionalità ${\displaystyle \left[M\right]\left[T\right]^{-3}\left[\Theta \right]^{-4}}$	${\displaystyle \sigma _{_{\sigma }{\text{P}}}={\frac {{P}_{\text{P}}}{{l}_{\text{P}}^{2}{\Theta }_{\text{P}}^{4}}}={\frac {{k}_{\text{B}}^{4}}{{\hbar }^{3}{c}^{2}}}={\frac {{16}\pi ^{4}\hbar {c}^{2}}{C_{2}^{4}}}}$		${\displaystyle 3,447174\cdot 10^{-7}{\frac {\mathrm {W} }{m^{2}\cdot \mathrm {K} ^{4}}}}$
Proprietà radioattive
Attività specifica di Planck	Attività specifica ${\displaystyle \left[T\right]^{-1}}$	${\displaystyle {\frac {1}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{4\pi \hbar G}}}}$	${\displaystyle {\frac {1}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}}$	${\displaystyle 5,232458\cdot 10^{42}\mathrm {Bq} }$	${\displaystyle 1,854858\cdot 10^{43}\mathrm {Bq} }$
Esposizione radioattiva di Planck	Radiazioni ionizzanti ${\displaystyle \left[M\right]^{-1}\left[Q\right]}$	${\displaystyle q_{r_{\text{s}}}={\frac {q_{\text{P}}}{m_{\text{P}}}}={\sqrt {\frac {2\pi {r_{\text{s}}}}{\mu _{0}}}}={\sqrt {\frac {G}{k_{e}}}}={\sqrt {4\pi \varepsilon _{0}G}}}$		${\displaystyle 8,617\;518\cdot 10^{-11}\;{\frac {\mathrm {C} }{kg}}}$
Potenziale gravitazionale di Planck	calorie specifiche ${\displaystyle \left[L\right]^{2}\left[T\right]^{-2}}$	${\displaystyle {\Phi _{_{G}}}_{\text{P}}={\frac {E_{\text{P}}}{m_{\text{P}}}}=c^{2}}$		${\displaystyle 89.875.517.873.681.764\;{\frac {\mathrm {J} }{kg}}}$
Dose assorbita di Planck	Dose assorbita ${\displaystyle \left[L\right]^{2}\left[T\right]^{-2}}$	${\displaystyle {\Phi _{_{G}}}_{\text{P}}={\frac {E_{\text{P}}}{m_{\text{P}}}}=c^{2}}$		${\displaystyle 8,987552\cdot 10^{16}\;\mathrm {Gy} }$
Velocità di dose assorbita di Planck	Velocità di dose assorbita ${\displaystyle \left[L\right]^{2}\left[T\right]^{-3}}$	${\displaystyle {\frac {{\Phi _{_{G}}}_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{9}}{4\pi \hbar G}}}}$	${\displaystyle {\frac {{\Phi _{_{G}}}_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{9}}{\hbar G}}}}$	${\displaystyle 4,702700\cdot 10^{59}\;{\frac {\mathrm {Gy} }{s}}}$	${\displaystyle 1,667064\cdot 10^{60}\;{\frac {\mathrm {Gy} }{s}}}$
Proprietà dei buchi neri
Massa lineare di Planck	Massa lineare ${\displaystyle \left[M\right]\left[L\right]^{-1}}$	${\displaystyle {l_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{l_{\text{P}}}}={\frac {2}{4\pi r_{s}}}={\frac {c^{2}}{4\pi G}}}$	${\displaystyle {l_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{l_{\text{P}}}}={\frac {2}{r_{s}}}={\frac {c^{2}}{G}}}$	${\displaystyle 1,071583\cdot 10^{26}\;{\frac {kg}{m}}}$	${\displaystyle 1,346591\cdot 10^{27}\;{\frac {kg}{m}}}$
Impedenza meccanica di Planck	Impedenza meccanica ${\displaystyle \left[M\right]\left[L\right]^{-1}}$	${\displaystyle {t_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{t_{\text{P}}}}={\frac {2c}{4\pi r_{s}}}={\frac {c^{3}}{4\pi G}}}$	${\displaystyle {t_{r}}_{\text{s}}^{-1}={\frac {m_{\text{P}}}{l_{\text{P}}}}={\frac {2c}{r_{s}}}={\frac {c^{3}}{G}}}$	${\displaystyle 3,212525\cdot 10^{34}\;{\frac {kg}{s}}}$	${\displaystyle 4,036978\cdot 10^{35}\;{\frac {kg}{s}}}$
Gravità di superficie	Gravità di superficie ${\displaystyle \left[L\right]\left[M\right]\left[T\right]^{-2}}$	${\displaystyle {a_{r}}_{\text{s}}\equiv {\frac {1}{4M}}\equiv {\frac {F_{\text{P}}}{{m_{r}}_{\text{s}}}}={\frac {m_{\text{P}}c}{t_{\text{P}}}}={\frac {c^{4}}{4\pi G}}}$	${\displaystyle {a_{r}}_{\text{s}}\equiv {\frac {1}{4M}}\equiv {\frac {F_{\text{P}}}{{m_{r}}_{\text{s}}}}={\frac {m_{\text{P}}c}{t_{\text{P}}}}={\frac {c^{4}}{G}}}$	${\displaystyle 9,630908\cdot 10^{42}{\frac {kg\cdot m}{s^{2}}}}$	${\displaystyle 1,210256\cdot 10^{44}{\frac {kg\cdot m}{s^{2}}}}$
Costante di accoppiamento di Planck	Teoria dell'informazione (adimensionale)	${\displaystyle {\alpha _{G}}_{\text{P}}={m_{r}}_{\text{s}}^{2}=\left({\frac {m_{\text{P}}}{m_{\text{P}}}}\right)^{2}={\frac {4\pi Gm_{\text{P}}^{2}}{\hbar c}}}$	${\displaystyle {\alpha _{G}}_{\text{P}}={m_{r}}_{\text{s}}^{2}=\left({\frac {m_{\text{P}}}{m_{\text{P}}}}\right)^{2}={\frac {Gm_{\text{P}}^{2}}{\hbar c}}}$	1	1
Limite di Bekenstein di Planck[6][7][8]	Teoria dell'informazione (adimensionale)	${\displaystyle {I_{_{bits}}}_{\text{P}}\leq {\frac {2\pi {\alpha _{G}}_{\text{P}}}{\log[2]}}={\frac {2\pi l_{\text{P}}E_{\text{P}}}{\hbar c}}}$		${\displaystyle 9,064720\ldots \mathrm {bits} }$${\displaystyle \approx 2^{3,18}}$ ${\displaystyle \approx 1,133\,\mathrm {bytes} }$
Rapporto massa-massa di Planck	Teoria dell'informazione (adimensionale)	${\displaystyle {m_{r}}_{\text{s}}={\frac {m_{\text{P}}}{m_{\text{P}}}}}$		${\displaystyle 1}$
Unità di Planck	Unita di Planck (adimensionale)	${\displaystyle {\sqrt {{\alpha _{G}}_{\text{P}}}}={m_{r}}_{\text{s}}={\frac {m_{\text{P}}}{m_{\text{P}}}}}$	${\displaystyle {\sqrt {{\alpha _{G}}_{\text{P}}}}={m_{r}}_{\text{s}}={\frac {m_{\text{P}}}{m_{\text{P}}}}}$	${\displaystyle 1}$	${\displaystyle 1}$

Nota: ${\displaystyle k_{e}}$ è la costante di Coulomb, ${\displaystyle \mu _{0}}$ è la permeabilità nel vuoto, ${\displaystyle Z_{0}}$ è l'impedenza di spazio libero, ${\displaystyle Y_{0}}$ è l'ammissione di spazio libero, ${\displaystyle R}$ è la costante dei gas.

Nota: ${\displaystyle N_{\text{A}}}$ è la costante di Avogadro, anch'essa normalizzata a ${\displaystyle 1}$ in entrambe le versioni di unità di Planck.

Note

1. (EN) Units, natural units and metrology, su The Spectrum of Riemannium. URL consultato il 22 marzo 2020.
2. www.espenhaug.com, su espenhaug.com. URL consultato il 22 marzo 2020.
3. Derived Planck Units - CODATA 2014 (PNG), su upload.wikimedia.org.
4. Alexander Bolonkin, Universe. Relations Between Time, Matter, Volume, Distance and Energy. Rolling Space, Time, Matter Into Point. URL consultato il 22 marzo 2020.
5. Relations between Charge, Time, Matter, Volume, Distance, and Energy (PDF), su pdfs.semanticscholar.org.
6. (EN) Los Alamos National Laboratory, Operated by Los Alamos National Security, LLC, for the U. S. Department of Energy, System Unavailable, su lanl.gov. URL consultato il 5 aprile 2020.
7. (EN) Jacob D. Bekenstein, Bekenstein bound, in Scholarpedia, vol. 3, n. 10, 31 ottobre 2008, p. 7374, DOI:10.4249/scholarpedia.7374. URL consultato il 5 aprile 2020.
8. (EN) Jacob D. Bekenstein, Bekenstein-Hawking entropy, in Scholarpedia, vol. 3, n. 10, 31 ottobre 2008, p. 7375, DOI:10.4249/scholarpedia.7375. URL consultato il 5 aprile 2020.

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