Library defined units and format

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Format IO

std::ostream adaptor operator << is defined in header <dimensional/io.hpp>.

example

// begin example
#include <dimensional/quantity.hpp>
#include <dimensional/systems/si/all.hpp>
#include <dimensional/io.hpp>

int main() {
    using mitama::quantity_t;
    namespace si = mitama::systems::si;

    quantity_t a = 1 | si::meters;

    std::cout << a << '\n'; // 1 [m]
}
// end example

SI basic units

type name quantifier name	Unit symbol	Quantity measured
metre_t/meter_t metre/meter	m	length
kilogram_t kilogram	kg	mass
second_t second	s	time
ampere_t ampere	A	electric current
kelvin_t kelvin	K	temperature
mole_t mole	mol	amount of substance
candela_t candela	cd	luminous intensity

Non SI units

type name quantifier name	Unit symbol	Equivalents in terms of SI units
hectare_t hectare	ha	$$1\ ha = 10^4\ m^2$$
litre_t/liter_t litre/liter	L	$$1\ L = 10^{-3}\ m^3$$
tonne_t tonne	t	$$1\ t = 10^3\ kg$$
au_t au	au	$$1\ au = 149,597,870,700\ m$$
minute_t minutes	min	$$1\ min = 60\ s$$
hour_t hours	h	$$1\ h = 60\ min = 3600\ s$$
day_t days	d	$$1\ d = 24\ h = 86400\ s$$

Named units derived from SI base units

type name quantifier Name	Symbol	Quantity	Equivalents	SI base unit Equivalents
hertz_t hertz	Hz	frequency	$$1/s$$	$$s^{-1}$$
radian_t radian	rad	angle	$$m/m$$	$$1$$
steradian_t steradian	sr	solid angle	$$m^2/m^2$$	$$1$$
newton_t newton	N	force weight	$$kg \cdot m/s^2$$	$$kg \cdot m \cdot s^{-2}$$
pascal_t pascal	Pa	pressure stress	$$N/m^2$$	$$kg \cdot m^{-1} \cdot s^{-2}$$
joule_t joule	J	energy work heat	$$N \cdot m \\ C \cdot V \\ W \cdot s$$	$$kg \cdot m^2 \cdot s^{-2}$$
watt_t watt	W	power radiant flux	$$J/s \\ V \cdot A$$	$$kg \cdot m^2 \cdot s^{-3}$$
coulomb_t coulomb	C	electric charge quantity of electricity	$$s \cdot A \\ F \cdot V$$	$$s \cdot A$$
volt_t volt	V	voltage electrical potential difference	$$W/A \\ J/C$$	$$kg \cdot m^2 \cdot s^{-3} \cdot A^{-1}$$
farad_t farad	F	electrical capacitance	$$C/V \\ s/\Omega$$	$$kg^{-1} \cdot m^{-2} \cdot s^4 \cdot A^2$$
ohm_t ohm	$$\Omega$$	electrical resistance impedance, reactance	$$1/S \\ V/A$$	$$kg \cdot m^2 \cdot s^{-3} \cdot A^{-2}$$
siemens_t siemens	S	electrical conductance	$$1/\Omega \\ A/V$$	$$kg^{-1} \cdot m^{-2} \cdot s^3 \cdot A^2$$
weber_t weber	Wb	magnetic flux	$$J/A \\ T \cdot m^2$$	$$kg \cdot m^2 \cdot s^{-2} \cdot A^{-1}$$
tesla_t tesla	T	magnetic induction magnetic flux density	$$V \cdot s/m^2 \\ Wb/m^2 \\ N/(A \cdot m)$$	$$kg \cdot s^{-2} \cdot A^{-1}$$
henry_t henry	H	electrical inductance	$$V \cdot s/A \\ \Omega \cdot s \\ Wb/A$$	$$kg \cdot m^2 \cdot s^{-2} \cdot A^{-2}$$
degree_celsius_t degree_celsius	°C	temperature relative to 273.15 K	$$K$$	$$K$$
lumen_t lumen	lm	luminous flux	$$cd \cdot sr$$	$$cd$$
lux_t lux	lx	illuminance	$$lm/m^2$$	$$m^{-2} \cdot cd$$
becquerel_t becquerel	Bq	radioactivity (decays per unit time)	$$1/s$$	$$s^{-1}$$
gray_t gray	Gy	absorbed dose (of ionizing radiation)	$$J/kg$$	$$m^2 \cdot s^{-2}$$
sievert_t sievert	Sv	equivalent dose (of ionizing radiation)	$$J/kg$$	$$m^2 \cdot s^{-2}$$
katal_t katal	kat	catalytic activity	$$mol/s$$	$$s^{-1} \cdot mol$$

Kinematic SI derived units

type name quantifier Name	Symbol	Expression in termsof SI base units
velocity_t velocity	$$m/s$$	$$m \cdot s^{-1}$$
acceleration_t acceleration	$$m/s^2$$	$$m \cdot s^{-2}$$
jerk_t jerk	$$m/s^3$$	$$m \cdot s^{-3}$$
snap_t snap	$$m/s^4$$	$$m \cdot s^{-4}$$
crackle_t crackle	$$m/s^5$$	$$m \cdot s^{-5}$$
pop_t pop	$$m/s^6$$	$$m \cdot s^{-6}$$
angular_velocity_t angular_velocity	$$rad/s$$	$$s^{-1}$$
angular_acceleration_t angular_acceleration	$$rad/s^2$$	$$s^{-2}$$
frequency_drift_t frequency_drift	$$Hz/s$$	$$s^{-2}$$
volumetric_flow_t volumetric_flow	$$m^3/s$$	$$m^3 \cdot s^{-1}$$

Molar SI derived units

type name quantifier Name	Symbol	Expression in terms of SI base units
molarity_t molarity	$$mol/m^3$$	$$m^{-3} \cdot mol$$
molar_volume_t molar_volume_t	$$m^3/mol$$	$$m^3 \cdot mol^{-1}$$
molar_entropy_t molar_entropy	$$J/(K \cdot mol)$$	$$m^2 \cdot kg \cdot s^{-2} \cdot K^{-1} \cdot mol^{-1}$$
molar_heat_capacity_t molar_heat_capacity	$$J/(K \cdot mol)$$	$$m^2 \cdot kg \cdot s^{-2} \cdot K^{-1} \cdot mol^{-1}$$
molar_energy_t molar_energy	$$J/mol$$	$$m^2 \cdot kg \cdot s^{-2} \cdot mol^{-1}$$
molar_conductivity_t molar_conductivity	$$S \cdot m^2/mol$$	$$kg^{-1} \cdot s^3 \cdot A^2 \cdot mol^{-1}$$
molality_t molality	$$mol/kg$$	$$kg^{-1} \cdot mol$$
molar_mass_t molar_mass	$$kg/mol$$	$$kg \cdot mol^{-1}$$
catalytic_efficiency_t catalytic_efficiency	$$m^3/(mol \cdot s)$$	$$m^3 \cdot s^{-1} \cdot mol^{-1}$$

Electromagnetic SI derived units

type name quantifier Name	Symbol	Expression in terms of SI base units
electric_displacement_field_t electric_displacement_field	$$C/m^2$$	$$m^{-2} \cdot s \cdot A$$
polarization_density_t polarization_density	---	$$m^{-2} \cdot s \cdot A$$
electric_charge_density_t electric_charge_density	$$C/m^3$$	$$m^{-3} \cdot s \cdot A$$
electric_current_density_t electric_current_density	$$A/m^2$$	$$m^{-2} \cdot A$$
electrical_conductivity_t electrical_conductivity	$$S/m$$	$$m^{-3} \cdot kg^{-1} \cdot s^3 \cdot A^2$$
permittivity_t permittivity	$$F/m$$	$$m^{-3} \cdot kg^{-1} \cdot s^4 \cdot A^2$$
permeability_t permeability	$$H/m$$	$$m \cdot kg \cdot s^{-2} \cdot A^{-2}$$
electric_field_strength_t electric_field_strength	$$V/m$$	$$m \cdot kg \cdot s^{-3} \cdot A^{-1}$$
magnetization_t magnetization	$$A/m$$	$$m^{-1} \cdot A$$
exposure_t exposure	$$C/kg$$	$$kg^{-1} \cdot s \cdot A$$
resistivity_t resistivity	$$\Omega \cdot m$$	$$m^3 \cdot kg \cdot s^{-3} \cdot A^{-2}$$
linear_charge_density_t linear_charge_density	$$C/m$$	$$m^{-1} \cdot s \cdot A$$
magnetic_dipole_moment_t magnetic_dipole_moment	---	$$m^2 \cdot A$$
electron_mobility_t electron_mobility	$$m^2/(V \cdot s)$$	$$kg^{-1} \cdot s^2 \cdot A$$
magnetic_reluctance_t magnetic_reluctance	$$H^{-1}$$	$$m^{-2} \cdot kg^{-1} \cdot s^2 \cdot A^2$$
magnetic_vector_potential_t magnetic_vector_potential	$$Wb/m$$	$$m \cdot kg \cdot s^{-2} \cdot A^{-1}$$
magnetic_moment_t magnetic_moment	$$Wb \cdot m$$	$$m^3 \cdot kg \cdot s^{-2} \cdot A^{-1}$$
magnetic_rigidity_t magnetic_rigidity	$$T \cdot m$$	$$m \cdot kg \cdot s^{-2} \cdot A^{-1}$$
magnetomotive_force_t magnetomotive_force	---	$$A$$
magnetic_susceptibility_t magnetic_susceptibility	$$m/H$$	$$m^{-1} \cdot kg^{-1} \cdot s^2 \cdot A^2$$

Photometric SI derived units

type name quantifier Name	Symbol	Expression in terms of SI base units
luminous_energy_t luminous_energy	$$lm \cdot s$$	$$s \cdot cd \cdot sr$$
luminous_exposure_t luminous_energy	$$lx \cdot s$$	$$m^{-2} \cdot s \cdot cd \cdot sr$$
luminance_t luminous_energy	$$cd/m^2$$	$$m^{-2} \cdot cd$$
luminous_efficacy_t luminous_energy	$$lm/W$$	$$m^{-2} \cdot kg^{-1} \cdot s^3 \cdot cd \cdot sr$$

Thermodynamic SI derived units

type name quantifier Name	Symbol	Expression in terms of SI base units
heat_capacity_t specific_entropy	$$J/K$$	$$m^2 \cdot kg \cdot s^{-2} \cdot K^{-1}$$
entropy_t entropy	$$J/K$$	$$m^2 \cdot kg \cdot s^{-2} \cdot K^{-1}$$
specific_heat_capacity_t specific_heat_capacity	$$J/(K \cdot kg)$$	$$m^2 \cdot s^{-2} \cdot K^{-1}$$
specific_entropy_t specific_entropy	$$J/(K \cdot kg)$$	$$m^2 \cdot s^{-2} \cdot K^{-1}$$
thermal_conductivity_t thermal_conductivity	$$W/(m \cdot K)$$	$$m \cdot kg \cdot s^{-3} \cdot K^{-1}$$
thermal_resistance_t thermal_resistance	$$K/W$$	$$m^{-2} \cdot kg^{-1} \cdot s^3 \cdot K$$
thermal_expansion_coefficient_t thermal_expansion_coefficient	$$K^{-1}$$	$$K^{-1}$$
temperature_gradient_t temperature_gradient	$$K/m$$	$$m^{-1} \cdot K$$