Crate quantity

Expand description

Representation of quantites, i.e. of unit valued scalars and arrays.

The units are checked at compile time and can be arbitrarily complex. Additional to simple scalar quantities, it also provides utilities for vector valued quantities, based on the ndarray crate, where all entries share the same unit.

For details on the available methods, see the documentation of the Quantity struct.

§SI Base Units and Associated Constants

The module contains the seven SI base units and their associated, exact-valued constants.

Unit	Unit symbol	Quantity	Associated constant	Associated constant name	Associated constant value
SECOND	$\text{s}$	time	DVCS	Hyperfine transition frequency of Cs	$\Delta\nu_\text{Cs}=9192631770\,\text{Hz}$
METER	$\text{m}$	length	CLIGHT	Speed of light	$c=299792458\,\frac{\text{m}}{\text{s}}$
KILOGRAM	$\text{kg}$	mass	PLANCK	Planck constant	$h=6.62607015\times 10^{-34}\,\text{J}\cdot\text{s}$
AMPERE	$\text{A}$	electric current	QE	Elementary charge	$e=1.602176634\times 10^{-19}\,\text{C}$
KELVIN	$\text{K}$	thermodynamic temperature	KB	Boltzmann constant	$k_\text{B}=1.380649\times 10^{-23}\,\frac{\text{J}}{\text{K}}$
MOL	$\text{mol}$	amount of substance	NAV	Avogadro constant	$N_\text{A}=6.02214076\times 10^{23}\,\text{mol}^{-1}$
CANDELA	$\text{cd}$	luminous intensity	KCD	Luminous efficacy of $540\,\text{THz}$ radiation	$K_\text{cd}=683\,\frac{\text{lm}}{\text{W}}$

§Derived Units

Additionally, it contains the following derived units.

Unit	Unit symbol	Quantity	Definition
HERTZ	$\text{Hz}$	frequency	$\text{s}^{-1}$
NEWTON	$\text{N}$	force, weight	$\text{kg}\frac{\text{m}}{\text{s}^2}$
PASCAL	$\text{Pa}$	pressure, stress	$\frac{\text{N}}{\text{m}^2}$
JOULE	$\text{J}$	energy, work, heat	$\text{N}\text{m}$
WATT	$\text{W}$	power, radiant flux	$\frac{\text{J}}{\text{s}}$
COULOMB	$\text{C}$	electric charge	$\text{A}\text{s}$
VOLT	$\text{V}$	electrical potential difference	$\frac{\text{W}}{\text{A}}$
FARAD	$\text{F}$	capacitance	$\frac{\text{C}}{\text{V}}$
OHM	$\text{Ω}$	resistance, impedance, reactance	$\frac{\text{V}}{\text{A}}$
SIEMENS	$\text{S}$	electrical conductance	$\text{Ω}^{-1}$
WEBER	$\text{Wb}$	magnetic flux	$\text{V}\text{s}$
TESLA	$\text{T}$	magnetic flux density	$\frac{\text{Wb}}{\text{m}^2}$
HENRY	$\text{H}$	inductance	$\frac{\text{Wb}}{\text{A}}$

§Additional units

For convenience, a number of commonly used units that are not directly combinations of SI base units is also included. These constants simplify the specification of properties, that are not given in SI units. However, as the representation of quantities is unique, they do not appear in formatted outputs.

Unit	Unit symbol	Quantity	Definition
ANGSTROM	$\text{\AA}$	length	$10^{-10}\,\text{m}$
AMU	$\text{u}$	mass	$1.6605390671738466\times 10^{-27}\,\text{kg}$
AU	$\text{au}$	length	$149597870700\,\text{m}$
BAR	$\text{bar}$	pressure	$10^5\,\text{Pa}$
CALORIE	$\text{cal}$	energy	$4.184\,\text{J}$
CELSIUS	$^\circ\text{C}$	temperature	$t\,^\circ\text{C}=\left(t+273.15\right)\,\text{K}$
DAY	$\text{d}$	time	$86400\,\text{s}$
DEGREES	$^\circ$	angle	$\frac{\pi}{180}\,\text{rad}$
GRAM	$\text{g}$	mass	$10^{-3}\,\text{kg}$
HOUR	$\text{h}$	time	$3600\,\text{s}$
LITER	$\text{l}$	volume	$10^{-3}\,\text{m}^3$
MINUTE	$\text{min}$	time	$60\,\text{s}$
RADIANS	$\text{rad}$	angle

§Additional constants

Constant	Name	Symbol	Value
G	Gravitational constant	$G$	$6.6743\times 10^{-11}\,\frac{\text{m}^3}{\text{kg}\cdot\text{s}^2}$
RGAS	Ideal gas constant	$R=N_\text{Av}k_\text{B}$	$8.31446261815324\,\frac{\text{J}}{\text{mol}\cdot\text{K}}$

§Prefixes

All units can be combined with the following prefixes:

Prefix	Prefix symbol	value	Prefix	Prefix symbol	value
DECI	$\text{d}$	$10^{-1}$	DECA	$\text{da}$	$10^{1}$
CENTI	$\text{c}$	$10^{-2}$	HECTO	$\text{h}$	$10^{2}$
MILLI	$\text{m}$	$10^{-3}$	KILO	$\text{k}$	$10^{3}$
MICRO	$\text{µ}$	$10^{-6}$	MEGA	$\text{M}$	$10^{6}$
NANO	$\text{n}$	$10^{-9}$	GIGA	$\text{G}$	$10^{9}$
PICO	$\text{p}$	$10^{-12}$	TERA	$\text{T}$	$10^{12}$
FEMTO	$\text{f}$	$10^{-15}$	PETA	$\text{P}$	$10^{15}$
ATTO	$\text{a}$	$10^{-18}$	EXA	$\text{E}$	$10^{18}$
ZEPTO	$\text{z}$	$10^{-21}$	ZETTA	$\text{Z}$	$10^{21}$
YOCTO	$\text{y}$	$10^{-24}$	YOTTA	$\text{Y}$	$10^{24}$
RONTO	$\text{r}$	$10^{-27}$	RONNA	$\text{R}$	$10^{27}$
QUECTO	$\text{q}$	$10^{-30}$	QUETTA	$\text{Q}$	$10^{30}$

§Examples

Calculate pressure of an ideal gas.

let temperature = 25.0 * CELSIUS;
let volume = 1.5 * METER.powi::<P3>();
let moles = 75.0 * MOL;
let pressure = moles * RGAS * temperature / volume;
println!("{:.5}", pressure);            // 123.94785 kPa

Calculate the gravitational pull of the moon on the earth.

let mass_earth = 5.9724e24 * KILOGRAM;
let mass_moon = 7.346e22 * KILOGRAM;
let distance = 383.398 * KILO * METER;
let force = G * mass_earth * mass_moon / distance.powi::<P2>();
println!("{:.5e}", force);              // 1.99208e26 N

Calculate the pressure distribution in the atmosphere using the barometric formula. Array operations require the ndarray feature.

let z = Length::linspace(1.0 * METER, 70.0 * KILO * METER, 10);
let g = 9.81 * METER / SECOND.powi::<P2>();
let m = 28.949 * GRAM / MOL;
let t = 10.0 * CELSIUS;
let p0 = BAR;
let pressure = (-z.clone() * m * g).convert_to(RGAS * t).mapv(f64::exp) * p0;
for i in 0..10 {
    println!("z = {:8.5}   p = {:9.5}", z.get(i), pressure.get(i));
}
// z =  1.00000  m   p =  99.98794 kPa
// z =  7.77867 km   p =  39.12796 kPa
// z = 15.55633 km   p =  15.31182 kPa
// z = 23.33400 km   p =   5.99192 kPa
// z = 31.11167 km   p =   2.34480 kPa
// z = 38.88933 km   p = 917.58301  Pa
// z = 46.66700 km   p = 359.07479  Pa
// z = 54.44467 km   p = 140.51557  Pa
// z = 62.22233 km   p =  54.98750  Pa
// z = 70.00000 km   p =  21.51808  Pa

§Feature flags

Interoperability with other crates can be achieved by activating the following features:

ndarray — Use N-dimensional arrays from the ndarray crate as value of a quantity.
num-dual — Use generalized (hyper-)dual numbers from the [num-dual] crate as value of a quantity.
python — Directly use (scalar) quantities in Python interfaces through pyo3 and the si-units package.
python_numpy — Use scalar and array quantities in Python interfaces through pyo3, numpy, and the si-units package.
approx — Enable approximate comparisons through the approx crate.

Structs§

CELSIUS: Additional unit degrees Celsius
Quantity: Physical quantity with compile-time checked unit.

Constants§

AMPERE: SI base unit Ampere $\left(\text{A}\right)$
AMU: Additional unit unified atomic mass $\left(1\,\text{u}\approx 1.660539\times 10^{-27}\,\text{kg}\right)$
ANGSTROM: Additional unit Ångstrom $\left(1\,\text{\AA}=10^{-10}\,\text{m}\right)$
ATTO: Prefix atto $\left(\text{a}=10^{-18}\right)$
AU: Additional unit astronomical unit $\left(1\,\text{au}=149597870700\,\text{m}\right)$
BAR: Additional unit bar $\left(1\,\text{bar}=10^5\,\text{Pa}\right)$
CALORIE: Additional unit calorie $\left(1\,\text{cal}=4.184\,\text{J}\right)$
CANDELA: SI base unit candela $\left(\text{cd}\right)$
CENTI: Prefix centi $\left(\text{c}=10^{-2}\right)$
CLIGHT: Speed of light $\left(c=299792458\,\frac{\text{m}}{\text{s}}\right)$
COULOMB: Derived unit Coulomb $\left(1\,\text{C}=1\,\text{A}\cdot\text{s}\right)$
DAY: Additional unit day $\left(1\,\text{d}=86400,\text{s}\right)$
DECA: Prefix deca $\left(\text{da}=10^{1}\right)$
DECI: Prefix deci $\left(\text{d}=10^{-1}\right)$
DEGREES: Angle unit degrees $\left(1°=\frac{\pi}{180}\text{rad}\right)$
DVCS: Hyperfine transition frequency of Cs $\left(\Delta\nu_\text{Cs}=9192631770\,\text{Hz}\right)$
EXA: Prefix exa $\left(\text{E}=10^{18}\right)$
FARAD: Derived unit Farad $\left(1\,\text{F}=1\,\frac{\text{C}}{\text{V}}\right)$
FEMTO: Prefix femto $\left(\text{f}=10^{-15}\right)$
G: Gravitational constant $\left(G=6.6743\times 10^{-11}\,\frac{\text{m}^3}{\text{kg}\cdot\text{s}^2}\right)$
GIGA: Prefix giga $\left(\text{G}=10^{9}\right)$
GRAM: Additional unit gram $\left(1\,\text{g}=10^{-3}\,\text{kg}\right)$
HECTO: Prefix hecto $\left(\text{h}=10^{2}\right)$
HENRY: Derived unit Henry $\left(1\,\text{T}=1\,\frac{\text{Wb}}{\text{A}}\right)$
HERTZ: Derived unit Hertz $\left(1\,\text{Hz}=1\,\text{s}^{-1}\right)$
HOUR: Additional unit hour $\left(1\,\text{h}=3600,\text{s}\right)$
JOULE: Derived unit Joule $\left(1\,\text{J}=1\,\text{kg}\frac{\text{m}^2}{\text{s}^2}\right)$
KB: Boltzmann constant $\left(k_\text{B}=1.380649\times 10^{-23}\,\frac{\text{J}}{\text{K}}\right)$
KCD: Luminous efficacy of $540\,\text{THz}$ radiation $\left(K_\text{cd}=683\,\frac{\text{lm}}{\text{W}}\right)$
KELVIN: SI base unit Kelvin $\left(\text{K}\right)$
KILO: Prefix kilo $\left(\text{k}=10^{3}\right)$
KILOGRAM: SI base unit kilogram $\left(\text{kg}\right)$
LITER: Additional unit liter $\left(1\,\text{l}=10^{-3}\,\text{m}^3\right)$
MEGA: Prefix mega $\left(\text{M}=10^{6}\right)$
METER: SI base unit meter $\left(\text{m}\right)$
MICRO: Prefix micro $\left(\text{µ}=10^{-6}\right)$
MILLI: Prefix milli $\left(\text{m}=10^{-3}\right)$
MINUTE: Additional unit minute $\left(1\,\text{min}=60,\text{s}\right)$
MOL: SI base unit mol $\left(\text{mol}\right)$
NANO: Prefix nano $\left(\text{n}=10^{-9}\right)$
NAV: Avogadro constant $\left(N_\text{A}=6.02214076\times 10^{23}\,\text{mol}^{-1}\right)$
NEWTON: Derived unit Newton $\left(1\,\text{N}=1\,\text{kg}\frac{\text{m}}{\text{s}^2}\right)$
OHM: Derived unit Ohm $\left(1\,\text{Ω}=1\,\frac{\text{V}}{\text{A}}\right)$
PASCAL: Derived unit Pascal $\left(1\,\text{Pa}=1\,\frac{\text{kg}}{\text{m}\cdot\text{s}^2}\right)$
PETA: Prefix peta $\left(\text{P}=10^{15}\right)$
PICO: Prefix pico $\left(\text{p}=10^{-12}\right)$
PLANCK: Planck constant $\left(h=6.62607015\times 10^{-34}\,\text{J}\cdot\text{s}\right)$
QE: Elementary charge $\left(e=1.602176634\times 10^{-19}\,\text{C}\right)$
QUECTO: Prefix quecto $\left(\text{q}=10^{-30}\right)$
QUETTA: Prefix quetta $\left(\text{Q}=10^{30}\right)$
RADIANS: Angle unit radians $\left(\text{rad}\right)$
RGAS: Ideal gas constant $\left(R=8.31446261815324\,\frac{\text{J}}{\text{molK}}\right)$
RONNA: Prefix ronna $\left(\text{R}=10^{27}\right)$
RONTO: Prefix ronto $\left(\text{r}=10^{-27}\right)$
SECOND: SI base unit second $\left(\text{s}\right)$
SIEMENS: Derived unit Siemens $\left(1\,\text{S}=1\,\text{Ω}^{-1}\right)$
TERA: Prefix tera $\left(\text{T}=10^{12}\right)$
TESLA: Derived unit Tesla $\left(1\,\text{T}=1\,\frac{\text{Wb}}{\text{m}^2}\right)$
VOLT: Derived unit Volt $\left(1\,\text{V}=1\,\frac{\text{W}}{\text{A}}\right)$
WATT: Derived unit Watt $\left(1\,\text{J}=1\,\text{kg}\frac{\text{m}^2}{\text{s}^3}\right)$
WEBER: Derived unit Weber $\left(1\,\text{Wb}=1\,\text{V}\cdot\text{s}\right)$
YOCTO: Prefix yocto $\left(\text{y}=10^{-24}\right)$
YOTTA: Prefix yotta $\left(\text{Y}=10^{24}\right)$
ZEPTO: Prefix zepto $\left(\text{z}=10^{-21}\right)$
ZETTA: Prefix zetta $\left(\text{Z}=10^{21}\right)$

Type Aliases§

Acceleration
Action
Angle
Area
Capacitance
Charge
Compressibility
Current
Density
Diffusivity
Dimensionless
ElectricPotential
ElectricalConductance
Energy
Entropy
EntropyDensity
EntropyPerTemperature
Force
Frequency
HeatCapacityRate
HeatFlux
Inductance
Length
LuminousIntensity
MagneticFlux
MagneticFluxDensity
Mass
MassDensity
MassFlowRate
MassFlux
MolarEnergy
MolarEntropy
MolarVolume
MolarWeight
MoleFlowRate
Moles
Power
Pressure
PressurePerTemperature
PressurePerVolume
Resistance
SIUnit
SpecificEnergy
SpecificEntropy
SurfaceTension
Temperature
ThermalConductivity
ThermalResistance
ThermalTransmittance
Time
Velocity
Viscosity
Volume
_Acceleration
_Action
_Area
_Capacitance
_Charge
_Compressibility
_Current
_Density
_Diffusivity
_Dimensionless
_ElectricPotential
_ElectricalConductance
_Energy
_Entropy
_EntropyDensity
_EntropyPerTemperature
_Force
_Frequency
_HeatCapacityRate
_HeatFlux
_Inductance
_Length
_LuminousIntensity
_MagneticFlux
_MagneticFluxDensity
_Mass
_MassDensity
_MassFlowRate
_MassFlux
_MolarEnergy
_MolarEntropy
_MolarVolume
_MolarWeight
_MoleFlowRate
_Moles
_Power
_Pressure
_PressurePerTemperature
_PressurePerVolume
_Resistance
_SpecificEnergy
_SpecificEntropy
_SurfaceTension
_Temperature
_ThermalConductivity
_ThermalResistance
_ThermalTransmittance
_Time
_Velocity
_Viscosity
_Volume

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