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Derived Physical Constants
Dimension
Derived constant
SI value
Length
L = (Gh/c3)1/2
4.05 x 10-35 m
Area
A = Gh/c3
1.64 x 10-69 m2
Volume
V = (G3h3/c9)1/2
6.64 x 10-104 m3
Time
t = (Gh/c5)1/2
1.35 x 10-43 s
Mass
m = hc/G
5.46 x 10-8 kg
Mass density
ρm = c5/G2h
8.24 x 1095 kg/m3
Velocity
v = c
3.00 x 108 m/s
Acceleration
a = (c7/Gh)1/2
2.22 x 1051 m/s2
Force
F = c4/G
1.21 x 1044 N
Pressure
P = c7/G2h
7.41 x 10112 Pa
Linear momentum
p = (hc3/G)1/2
1.64 x 101 N s
Angular momentum
l = h
6.63 x 10-34 J s
Energy
E = (hc5/G)1/2
4.91 x 109 J
Gravitational potential
Vg = c2
9.00 x 1016 m2/s2
Power
P = c5/G
3.64 x 1052 W
Radiation flux
F = c8/G2h
2.22 x 10121 W/m2
Electric charge
Q = e
1.60 x 10-19 C
Electric charge
Q = (h/cμo)1/2
1.32 x 10-18 C
Charge density
ρe = (e2c9/G3h3)1/2
2.41 x 1084 C/m3
Electric current
I = (e2c5/Gh)1/2
1.19 x 1024 A
Current density
J = (e2c11/G3h3)1/2
7.24 x 1092 A/m2
Electric field
E = c4/Ge
7.59 x 1062 N/C
Magnetic field
B = c3/Ge
2.53 x 1054 T
Electric potential
V = (hc5/Ge2)1/2
3.90 x 1015 V
Magnetic potential
Amag= (hc3/Ge2)1/2
1.02 x 1020
T m
Electric dipole moment
μe= (Ghe2/c3)1/2
6.48 x 10-54 C m
Magnetic dipole moment
μmag= (Ghe2/c)1/2
1.94 x 10-45 C m2/s
Electric resistance
R = h/e2
2.59 x 104 O
Capacitance
C = (Ge4/hc5)1/2
5.21 x 10-48 F
Magnetic flux
θB= h/e
4.14 x 10-15 T m2
Inductance
H = (Gh3/e4c5)1/2
3.49 x 10-39 H
