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Unità di misura di Planck derivate - Wikipedia

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(Reindirizzamento da Corrente di Planck)

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.

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

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

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

^ (EN) Units, natural units and metrology, su The Spectrum of Riemannium. URL consultato il 22 marzo 2020.
^ www.espenhaug.com, su espenhaug.com. URL consultato il 22 marzo 2020.
^ Derived Planck Units - CODATA 2014 (PNG), su upload.wikimedia.org.
^ Alexander Bolonkin, Universe. Relations Between Time, Matter, Volume, Distance and Energy. Rolling Space, Time, Matter Into Point. URL consultato il 22 marzo 2020.
^ Relations between Charge, Time, Matter, Volume, Distance, and Energy (PDF), su pdfs.semanticscholar.org.
^ (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.
^ (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.
^ (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.