HEP System

Namespace: mp_units::hep

Module: mp_units.systems

Header: <mp-units/systems/hep.h>

Secondary Headers:

• <mp-units/systems/hep/constants.h>
• <mp-units/systems/hep/quantities.h>
• <mp-units/systems/hep/units.h>

Dimensions

Name	Symbol
dim_amount_of_substance	N
dim_angle	α
dim_electric_charge	Q
dim_energy	E
dim_length	L
dim_luminous_intensity	I
dim_temperature	Θ
dim_time	T

Quantities

Quantity	Character	Dimension	Traits	Kind of	Parent	Equation	Hierarchy
Q_value	scalar	E	≥ 0	energy	energy	—	view
absorbed_dose	scalar	L²T⁻²	kind	absorbed_dose	—	pow<2>(length) / pow<2>(duration)	view
activity	scalar	T⁻¹	kind	activity	—	inverse(duration)	view
amount_of_substance	scalar	N	kind ≥ 0	amount_of_substance	—	—	view
angle	scalar	—		—	—	alias to angular::angle	—
area	scalar	L²	kind	area	—	pow<2>(length)	view
azimuthal_angle	scalar	α		angular::angle	angular::angle	—	view
binding_energy	scalar	E	≥ 0	energy	energy	—	view
center_of_mass_energy	scalar	E	≥ 0	energy	energy	—	view
coordinate_time	scalar	T	kind ≥ 0	coordinate_time	duration	—	view
cross_section	scalar	L²		area	area	—	view
decay_constant	scalar	T⁻¹	kind	decay_constant	—	inverse(duration)	view
decay_length	scalar	L	≥ 0	length	length	—	view
dimensionless	scalar	1	kind	dimensionless	—	—	—
displacement	vector	L		length	length	—	view
duration	scalar	T	kind ≥ 0	duration	—	—	view
effective_mass	scalar	ET²L⁻²		mass	mass	—	view
electric_capacitance	scalar	Q²E⁻¹	kind	electric_capacitance	—	pow<2>(electric_charge) / energy	view
electric_charge	scalar	Q	kind	electric_charge	—	—	view
electric_current	scalar	QT⁻¹	kind	electric_current	—	electric_charge / duration	view
electric_potential	scalar	EQ⁻¹	kind	electric_potential	—	energy / electric_charge	view
electric_resistance	scalar	ETQ⁻²	kind	electric_resistance	—	energy * duration / pow<2>(electric_charge)	view
energy	scalar	E	kind ≥ 0	energy	—	—	view
excitation_energy	scalar	E	≥ 0	energy	energy	—	view
force	scalar	EL⁻¹	kind	force	—	energy / length	view
frequency	scalar	T⁻¹	kind	frequency	—	inverse(duration)	view
half_life	scalar	T	≥ 0	duration	lifetime	—	view
height	scalar	L	≥ 0	length	length	—	view
illuminance	scalar	α²IL⁻²	kind	illuminance	—	luminous_flux / pow<2>(length)	view
impact_parameter	scalar	L	≥ 0	length	length	—	view
inductance	scalar	ET²Q⁻²	kind	inductance	—	pow<2>(duration) * energy / pow<2>(electric_charge)	view
interaction_length	scalar	L	kind ≥ 0	interaction_length	length	—	view
invariant_mass	scalar	ET²L⁻²		mass	mass	—	view
ionization_energy	scalar	E	≥ 0	energy	energy	—	view
kinetic_energy	scalar	E	≥ 0	energy	total_energy	—	view
length	scalar	L	kind ≥ 0	length	—	—	view
lifetime	scalar	T	≥ 0	duration	duration	—	view
lorentz_factor	scalar	—	kind ≥ 0	lorentz_factor	dimensionless	—	view
luminous_flux	scalar	α²I	kind	luminous_flux	—	luminous_intensity * solid_angle	view
luminous_intensity	scalar	I	kind ≥ 0	luminous_intensity	—	—	view
magnetic_field	scalar	ETQ⁻¹L⁻²	kind	magnetic_field	—	duration * energy / electric_charge / pow<2>(length)	view
magnetic_flux	scalar	ETQ⁻¹	kind	magnetic_flux	—	duration * energy / electric_charge	view
mass	scalar	ET²L⁻²	kind	mass	—	energy * pow<2>(duration) / pow<2>(length)	view
mean_free_path	scalar	L	≥ 0	length	length	—	view
mean_lifetime	scalar	T	≥ 0	duration	lifetime	—	view
missing_energy	scalar	E	≥ 0	energy	energy	—	view
momentum	scalar	ETL⁻¹	kind	momentum	—	energy * duration / length	view
nuclear_interaction_length	scalar	L	≥ 0	interaction_length	interaction_length	—	view
number_density	scalar	L⁻³	kind	number_density	—	inverse(volume)	view
opening_angle	scalar	α		angular::angle	angular::angle	—	view
path_length	scalar	L	≥ 0	length	length	—	view
phase	scalar	—	kind	phase	dimensionless	—	view
polar_angle	scalar	α		angular::angle	angular::angle	—	view
position_vector	vector	L		length	displacement	—	view
power	scalar	ET⁻¹	kind	power	—	energy / duration	view
pressure	scalar	EL⁻³	kind	pressure	—	energy / pow<3>(length)	view
proper_time	scalar	T	kind ≥ 0	proper_time	duration	—	view
proper_velocity	vector	LT⁻¹	kind	proper_velocity	—	displacement / proper_time	view
radiation_length	scalar	L	kind ≥ 0	radiation_length	length	—	view
radius	scalar	L	≥ 0	length	length	—	view
range	scalar	L	≥ 0	length	length	—	view
reduced_mass	scalar	ET²L⁻²		mass	mass	—	view
relativistic_beta	scalar	—	kind ≥ 0	relativistic_beta	dimensionless	—	view
rest_mass	scalar	ET²L⁻²		mass	mass	—	view
rest_mass_energy	scalar	E	≥ 0	energy	total_energy	—	view
scattering_angle	scalar	α		angular::angle	angular::angle	—	view
separation_energy	scalar	E	≥ 0	energy	binding_energy	—	view
solid_angle	scalar	—		—	—	alias to angular::solid_angle	—
speed	scalar	LT⁻¹	kind	speed	—	length / duration	view
temperature	scalar	Θ	kind ≥ 0	temperature	—	—	view
threshold_energy	scalar	E	≥ 0	energy	energy	—	view
time_of_flight	scalar	T	≥ 0	duration	duration	—	view
total_energy	scalar	E	≥ 0	energy	energy	—	view
transverse_energy	scalar	E	≥ 0	energy	energy	—	view
transverse_momentum	scalar	ETL⁻¹		momentum	momentum	—	view
velocity	vector	LT⁻¹		speed	speed	displacement / duration	view
vertex_position	scalar	L	≥ 0	length	length	—	view
volume	scalar	L³	kind	volume	—	pow<3>(length)	view
wavelength	scalar	L	≥ 0	length	length	—	view
width	scalar	L	≥ 0	length	length	—	view

Units

Unit Name	Symbol	unit_symbol	Definition
ampere	A	—	coulomb / second
angstrom	Å (A)	—	mag_power<10, -10> * meter
astronomical_unit	au	—	mag<149'597'870'700> * meter
atmosphere	atm	—	mag<101'325> * pascal
bar	bar	—	mag_power<10, 5> * pascal
barn	b	b	mag_power<10, -28> * square(meter)
becquerel	Bq	Bq	one / second kind: activity
candela	cd	—	kind: luminous_intensity
coulomb	C	—	mag<6'241'509'074> * mag_power<10, 9> * eplus
curie	Ci	Ci	mag_ratio<37, 10> * mag_power<10, 10> * becquerel
degree	° (deg)	deg	alias to angular::degree
electronvolt	eV	eV	kind: energy
eplus	e⁺ (e+)	—	kind: electric_charge
farad	F	—	coulomb / volt
fermi	—	—	si::femto<meter>
gauss	G	—	mag_power<10, -4> * tesla
gradian	ᵍ (grad)	grad	alias to angular::gradian
gram	g	g	mag_ratio<1, 1000> * joule * square(second) / square(meter)
gray	Gy	—	joule / si::kilo<gram> kind: absorbed_dose
halfpi	—	—	mag_ratio<1, 2> * pi
henry	H	—	weber / ampere
hertz	Hz	—	one / second kind: frequency
joule	J	—	electronvolt * coulomb / eplus
kelvin	K	—	kind: temperature
liter	L	L	cubic(si::deci<meter>)
lumen	lm	—	candela * steradian
lux	lx	—	lumen / square(meter)
meter	m	m	kind: length
mole	mol	—	kind: amount_of_substance
newton	N	—	joule / meter
ohm	Ω (ohm)	—	volt / ampere
parsec	pc	pc	astronomical_unit / (mag_ratio<1, 3600> * degree)
pascal	Pa	—	newton / square(meter)
perCent	%	—	alias to mp_units::percent
perMillion	ppm	—	alias to mp_units::parts_per_million
perThousand	‰ (%o)	—	alias to mp_units::per_mille
radian	rad	rad	alias to angular::radian
revolution	rev	rev	alias to angular::revolution
second	s	s	kind: duration
steradian	sr	sr	alias to angular::steradian
tesla	T	—	weber / square(meter)
twopi	—	—	mag<2> * pi
volt	V	—	electronvolt / eplus
watt	W	—	joule / second
weber	Wb	—	volt * second

Prefixed unit symbols

Not every unit has a symbol for every prefix. A combination that is not listed here does not exist, however reasonable it looks.

Unit	Prefixed symbols
barn	fb pb nb ub mb
becquerel	kBq MBq GBq
curie	uCi mCi
electronvolt	keV MeV GeV TeV PeV
gram	mg kg
liter	mL cL dL
meter	nm um mm cm km
radian	mrad
second	ps ns us ms

Constants

Name	Symbol	unit_symbol	Definition	Standard uncertainty
avogadro_constant	N_A	N_A	mag_ratio<602'214'076, 100'000'000> * mag_power<10, 23> / mole	—
codata2014::atomic_mass_unit	u	—	mag_ratio<9'314'940'954, 10'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<57, 10> * mag_power<10, -6> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2014::bohr_magneton	μ_B (mu_B)	—	mag_ratio<9'274'009'994, 1'000'000'000> * mag_power<10, -24> * joule / tesla	mag_ratio<57, 10> * mag_power<10, -32> * joule / tesla
codata2014::bohr_radius	a_0	—	mag_ratio<52'917'721'067, 10'000'000'000> * mag_power<10, -11> * meter	mag_ratio<12, 10> * mag_power<10, -21> * meter
codata2014::boltzmann_constant	k_B	—	mag_ratio<86'173'303, 10'000'000> * mag_power<10, -11> * si::mega<electronvolt> / kelvin	mag_ratio<50, 10> * mag_power<10, -17> * si::mega<electronvolt> / kelvin
codata2014::classical_electron_radius	r_e	—	mag_ratio<28'179'403'227, 10'000'000'000> * mag_power<10, -15> * meter	mag_ratio<19, 10> * mag_power<10, -24> * meter
codata2014::electron_compton_wavelength	λ_C (lambda_C)	—	mag_ratio<24'263'102'367, 10'000'000'000> * mag_power<10, -12> * meter	mag_ratio<11, 10> * mag_power<10, -21> * meter
codata2014::electron_mass	m_e	—	mag_ratio<5'109'989'461, 10'000'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<31, 10> * mag_power<10, -9> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2014::fine_structure_constant	α (alpha)	—	mag_ratio<72'973'525'664, 10'000'000'000> * mag_power<10, -3> * one	mag_ratio<17, 10> * mag_power<10, -12> * one
codata2014::neutron_mass	m_n	—	mag_ratio<9'395'654'133, 10'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<58, 10> * mag_power<10, -6> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2014::nuclear_magneton	μ_N (mu_N)	—	mag_ratio<5'050'783'699, 1'000'000'000> * mag_power<10, -27> * joule / tesla	mag_ratio<31, 10> * mag_power<10, -35> * joule / tesla
codata2014::permeability_of_vacuum	μ₀ (mu_0)	—	mag<4> * mag_power<10, -7> * π * henry / meter	—
codata2014::proton_mass	m_p	—	mag_ratio<9'382'720'813, 10'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<58, 10> * mag_power<10, -6> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2018::atomic_mass_unit	u	u	mag_ratio<93'149'410'242, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<28, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2018::bohr_magneton	μ_B (mu_B)	mu_B	mag_ratio<92'740'100'783, 10'000'000'000> * mag_power<10, -24> * joule / tesla	mag_ratio<28, 10> * mag_power<10, -33> * joule / tesla
codata2018::bohr_radius	a_0	a_0	mag_ratio<529'177'210'903, 100'000'000'000> * mag_power<10, -11> * meter	mag_ratio<80, 10> * mag_power<10, -21> * meter
codata2018::boltzmann_constant	k_B	k_B	mag_ratio<8'617'333'262, 1'000'000'000> * mag_power<10, -11> * si::mega<electronvolt> / kelvin	—
codata2018::classical_electron_radius	r_e	r_e	mag_ratio<28'179'403'262, 10'000'000'000> * mag_power<10, -15> * meter	mag_ratio<13, 10> * mag_power<10, -24> * meter
codata2018::electron_compton_wavelength	λ_C (lambda_C)	lambda_C	mag_ratio<242'631'023'867, 100'000'000'000> * mag_power<10, -12> * meter	mag_ratio<73, 10> * mag_power<10, -22> * meter
codata2018::electron_mass	m_e	m_e	mag_ratio<51'099'895, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<15, 10> * mag_power<10, -10> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2018::fine_structure_constant	α (alpha)	alpha	mag_ratio<72'973'525'693, 10'000'000'000> * mag_power<10, -3> * one	mag_ratio<11, 10> * mag_power<10, -12> * one
codata2018::neutron_mass	m_n	m_n	mag_ratio<93'956'542'052, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<54, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2018::nuclear_magneton	μ_N (mu_N)	mu_N	mag_ratio<50'507'837'461, 10'000'000'000> * mag_power<10, -27> * joule / tesla	mag_ratio<15, 10> * mag_power<10, -36> * joule / tesla
codata2018::permeability_of_vacuum	μ₀ (mu_0)	mu_0	mag_ratio<125'663'706'212, 100'000'000'000> * mag_power<10, -6> * henry / meter	mag_ratio<19, 10> * mag_power<10, -16> * henry / meter
codata2018::proton_mass	m_p	m_p	mag_ratio<938'272'08816, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<29, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2022::atomic_mass_unit	u	—	mag_ratio<93'149'410'372, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<29, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2022::bohr_magneton	μ_B (mu_B)	—	mag_ratio<92'740'100'657, 10'000'000'000> * mag_power<10, -24> * joule / tesla	mag_ratio<29, 10> * mag_power<10, -33> * joule / tesla
codata2022::bohr_radius	a_0	—	mag_ratio<529'177'210'544, 100'000'000'000> * mag_power<10, -11> * meter	mag_ratio<82, 10> * mag_power<10, -21> * meter
codata2022::boltzmann_constant	k_B	—	alias to codata2018::boltzmann_constant	—
codata2022::classical_electron_radius	r_e	—	mag_ratio<28'179'403'205, 10'000'000'000> * mag_power<10, -15> * meter	mag_ratio<13, 10> * mag_power<10, -24> * meter
codata2022::electron_compton_wavelength	λ_C (lambda_C)	—	mag_ratio<242'631'023'538, 100'000'000'000> * mag_power<10, -12> * meter	mag_ratio<76, 10> * mag_power<10, -22> * meter
codata2022::electron_mass	m_e	—	mag_ratio<51'099'895'069, 100'000'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<16, 10> * mag_power<10, -10> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2022::fine_structure_constant	α (alpha)	—	mag_ratio<72'973'525'643, 10'000'000'000> * mag_power<10, -3> * one	mag_ratio<11, 10> * mag_power<10, -12> * one
codata2022::neutron_mass	m_n	—	mag_ratio<93'956'542'194, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<48, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
codata2022::nuclear_magneton	μ_N (mu_N)	—	mag_ratio<50'507'837'393, 10'000'000'000> * mag_power<10, -27> * joule / tesla	mag_ratio<16, 10> * mag_power<10, -36> * joule / tesla
codata2022::permeability_of_vacuum	μ₀ (mu_0)	—	mag_ratio<125'663'706'127, 100'000'000'000> * mag_power<10, -6> * henry / meter	mag_ratio<20, 10> * mag_power<10, -16> * henry / meter
codata2022::proton_mass	m_p	—	mag_ratio<93'827'208'943, 100'000'000> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)	mag_ratio<29, 10> * mag_power<10, -7> * si::mega<electronvolt> / square(speed_of_light_in_vacuum)
elementary_charge	e	e	eplus	—
gas_threshold	gas_threshold	—	mag<10> * si::milli<gram> / cubic(si::centi<meter>)	—
pi	π (pi)	—	alias to mp_units::pi	—
planck_constant	h	h	mag_ratio<662'607'015, 100'000'000> * mag_power<10, -34> * joule * second	—
speed_of_light_in_vacuum	c	c	mag<299'792'458> * meter / second	—
standard_pressure	P_STP	—	atmosphere	—
standard_temperature	T_STP	—	mag_ratio<27'315, 100> * kelvin	—
universe_mean_density	ρ_universe (rho_universe)	—	mag_power<10, -25> * gram / cubic(si::centi<meter>)	—

Constants with a standard uncertainty are measured rather than exact by definition, and satisfy the MeasuredConstant concept. The uncertainty is stated in the form its source publishes: an absolute value in the constant's own dimension, or a relative one (marked (relative)) when only that form is published. A — means no uncertainty is declared for that constant.

Inline Namespaces

The mp_units::hep::codata2018 namespace is inline in mp_units::hep, making its members directly accessible from the parent namespace.