Systems of units

Each system of units is defined by giving a unit of angle, length, mass, time, electric current, temperature, luminous intensity, and quantity of matter. The systems of units implemented in the converter are defined as follows.

	Angle	Length	Mass	Time	Current	Temp.	Lumin. int.	Quant. of mat.
International	rad	m	kg	s	A	K	cd	mol
CGS	rad	cm	g	s	Gi	K	cd	mol
Atomic units	rad	a0	me	t0	I0	K	cd	mol
Relativistic	rad	lr	me	tr	Ir	K	cd	mol
Planck	rad	lP	mP	tP	IP	T_P	cd	mol
Am-eV	rad	Am	MA	tA	IA	TA	cd	mol

The units t0, I0, lr, tr, Ir, IP, MA, tA, IA, and TA are never used in practice. They solely serve to define systems of units with adequate properties.

Derived units of the International system are:

Symbol	Name	Dimension	Value
Hz	Hertz	Frequency	s^-1
d	Diopter	Inverse length	m^-1
C	Coulomb	Electric charge	s A
N	Newton	Force	m kg s^-2
J	Joule	Energy	m² kg s^-2
W	Watt	Power	m² kg s^-3
Pa	Pascal	Pressure	m^-1 kg s^-2
V	Volt	Electric potential	m² kg s^-3 A^-1
Ohm	Ohm	Electric resistance	m² kg s^-3 A^-2
S	Siemens	Electric conductance	m^-2 kg^-1 s³ A²
F	Faraday	Electric capacitance	m^-2 kg^-1 s⁴ A²
H	Henry	Inductance	m² kg s^-2 A^-2
T	Tesla	Magnetic field	kg s^-2A^-1
Wb	Weber	Magnetic flux	m² kg s^-2A^-1
Bq	Becquerel	Activity	s^-1
Gy	Gray	Dose of radiation	m² s^-2
kat	Katal	Catalytic activity	s^-1 mol
sterad	Steradian	Solid angle	rad²
lumen	Lumen	Light flux	rad² cd

Derived units of the CGS system are:

Symbol	Name	Dimension	Value
dyne	Dyne	Force	cm g s^-2
erg	Erg	Energy	cm² g s^-2
Oe	Oersted	Magnetic intensity	cm^-1 Gi
ph	Phot	Luminance	cm^-2 cd
St	Stokes	Cinematic viscosity	cm² s^-1
P	Poise	Absolute viscosity	cm^-1 g s^-1
kat	Katal	Catalytic activity	s^-1 mol
sterad	Steradian	Solid angle	rad²

Derived units of the Atomic units system are:

Symbol	Name	Dimension	Value
a0	Bohr radius	Length	a0
me	Electron mass	Mass	me
q	Elementary charge	Electric charge	t0 I0
hbar	Dirac constant	Action	a0² me t0^-1
Hr	Hartree	Energy	a0² me t0^-2
2 muB	Twice the Bohr magneton	Magnetic dipole	a0² I0
sterad	Steradian	Solid angle	rad²

Derived units of the Relativistic system are:

Symbol	Name	Dimension	Value
c	Speed of light in vacuum	Velocity	lr tr^-1
me	Electron mass	Mass	me
q	Elementary charge	Electric charge	tr Ir
hbar	Dirac constant	Action	lr² me tr^-1
2 muB	Twice the Bohr magneton	Magnetic dipole	lr² Ir
sterad	Steradian	Solid angle	rad²

Derived units of the Planck system are:

Symbol	Name	Dimension	Value
c	Speed of light in vacuum	Velocity	lP tP^-1
q	Elementary charge	Electric charge	tP IP
hbar	Dirac constant	Action	lP² mP tP^-1
k	Boltzmann constant	Entropy	IP² mP tP^-2T_P^-1
sterad	Steradian	Solid angle	rad²

Derived units of the Angstrom-eV system are:

Symbol	Name	Dimension	Value
Am	Angstrom	Length	Am
q	Elementary charge	Electric charge	tA IA
hbar	Dirac constant	Action	Am² MA tA^-1
k	Boltzmann constant	Entropy	Am² MA tA^-2TA^-1
eV	electron volt	Energy	Am² MA tA^-2
sterad	Steradian	Solid angle	rad²

Systems of units