Quantities and Units
One of the main goals of the CSD model is that the datasets are self contained to simplify sharing of scientific data. An essential part of achieving this goal is that all quantities in a dataset are specified as proper scientific quantities, i.e. as a number and a unit. The use of quantities is integrated in all parts of CSDM.
The supporting material of the CSDM paper give an extended overview of the units and quantities allowed in CSDM. Here is a brief summary of the quantities allowed in CSDM. Note that the current JavaScript implementation does not give correct units of dimensionless units arising from ratios of quantities, such as the plane angle with dimensionality L/L.
Test the unit parser here:
We are currently preparing generic libraries to handle quantities in other applications. You can see the status below.
| Language | Implemented | Available | Comment |
|---|---|---|---|
| Python | 😀 | 😀 | The csdmpy package is available. |
| JavaScript | 😀 | 😀 | Debugging is still undergoing, but take a preview at gitlab. |
| Tcl | 😀 | 😐 | As part of the SIMPSON implementaion of CSDM, we are developing a Tcl interface that is still under development. |
| Obj-C | 😀 | 😀 | Units and quantities are supported by RMN and PhySyCalc. The libraries are not available for download. |
| C | 😡 | 😡 | We are planning to translate the JavaScript implementation into a C library. More information will become available here later. |
😀: Fully implemented
😐: Partially implemented
😡: Not implemented
The entries of the table are the allowed quantities in CSDM.
| Quantity | SI unit | Dimensionality |
|---|---|---|
| length | m | L |
| mass | kg | M |
| time | s | T |
| electric current | A | I |
| thermodynamic temperature | K | Θ |
| amount of substance | mol | N |
| luminous intensity | cd | J |
| absorbed dose | m^2/s^2 | L^2*M/(M*T^2) |
| absorbed dose rate | m^2/s^3 | L^2/T^3 |
| absorption | ° | |
| acceleration | m/s^2 | L/T^2 |
| action | m^2*kg/s | L^2*M/T |
| amount | mol | N |
| amount concentration | mol/m^3 | N/L^3 |
| amount of electricity | s*A | T*I |
| amount ratio | ° | N/N |
| angle | ° | L/L |
| angular acceleration | 1/s^2 | L/(L*T^2) |
| angular frequency | Hz | L/(L*T) |
| angular momentum | m^2*kg/s | L^2*M/T |
| angular speed | Hz | L/(L*T) |
| angular velocity | Hz | L/(L*T) |
| area | m^2 | L^2 |
| area ratio | ° | L^2/L^2 |
| capacitance | s^4*A^2/(m^2*kg) | T^4*I^2/(L^2*M) |
| catalytic activity | mol/s | N/T |
| catalytic activity concentration | mol/(m^3*s) | N/(L^3*T) |
| catalytic activity content | mol/(kg*s) | N/(M*T) |
| charge to amount ratio | s*A/mol | T*I/N |
| charge to mass ratio | s*A/kg | T*I/M |
| circulation | m^2/s | L^2/T |
| compressibility | m*s^2/kg | L*T^2/M |
| current | A | I |
| current density | A/m^2 | I/L^2 |
| current ratio | ° | I/I |
| density | kg/m^3 | M/L^3 |
| diffusion coefficient | m^2/s | L^2/T |
| diffusion flux | mol/(m^2*s) | N/(L^2*T) |
| dimensionless | ° | 1 |
| distance per volume | 1/m^2 | L/L^3 |
| dose equivalent | m^2/s^2 | L^2*M/(M*T^2) |
| dynamic viscosity | kg/(m*s) | M/(L*T) |
| elastic modulus | Pa | M/(L*T^2) |
| electric charge | s*A | T*I |
| electric charge density | s*A/m^3 | T*I/L^3 |
| electric conductance | S | T^3*I^2/(L^2*M) |
| electric conductivity | s^3*A^2/(m^3*kg) | T^3*I^2/(L^3*M) |
| electric dipole moment | m*s*A | L*T*I |
| electric displacement | s*A/m^2 | T*I/L^2 |
| electric field gradient | kg/(s^3*A) | L^2*M/(L^2*T^3*I) |
| electric field strength | m*kg/(s^3*A) | L*M/(T^3*I) |
| electric flux | m^3*kg/(s*A) | L^3*M/(T*I) |
| electric flux density | s*A/m^2 | T*I/L^2 |
| electric polarizability | s^4*A^2/kg | L^2*T^4*I^2/(L^2*M) |
| electric potential difference | V | L^2*M/(T^3*I) |
| electric quadrupole moment | m^2*s*A | L^2*T*I |
| electric resistance | Ω | L^2*M/(T^3*I^2) |
| electric resistance per length | m*kg/(s^3*A^2) | L^2*M/(L*T^3*I^2) |
| electric resistivity | m^3*kg/(s^3*A^2) | L^3*M/(T^3*I^2) |
| electrical mobility | s^2*A/kg | L^2*T^3*I/(L^2*M*T) |
| electromotive force | V | L^2*M/(T^3*I) |
| energy | J | L^2*M/T^2 |
| energy density | Pa | M/(L*T^2) |
| entropy | m^2*kg/(s^2*K) | L^2*M/(T^2*Θ) |
| fine structure constant | ° | L^5*M*T^4*I^2/(L^5*M*T^4*I^2) |
| first hyperpolarizability | s^7*A^3/(m*kg^2) | L^3*T^7*I^3/(L^4*M^2) |
| fluidity | m*s/kg | L*T/M |
| force | N | L*M/T^2 |
| frequency | Hz | 1/T |
| frequency per electric field gradient | s^2*A/kg | L^2*T^3*I/(L^2*M*T) |
| frequency per electric field gradient squared | s^5*A^2/kg^2 | L^4*T^6*I^2/(L^4*M^2*T) |
| frequency per magnetic flux density | s*A/kg | T*I/M |
| frequency ratio | ° | T/T |
| gas permeance | s*mol/(m*kg) | L*T^2*N/(L^2*M*T) |
| gravitational constant | m^3/(kg*s^2) | L^3/(M*T^2) |
| gyromagnetic ratio | s*A/kg | L*T^2*I/(L*M*T) |
| heat capacity | m^2*kg/(s^2*K) | L^2*M/(T^2*Θ) |
| heat flux density | kg/s^3 | L^2*M/(L^2*T^3) |
| heat transfer coefficient | kg/(s^3*K) | M/(T^3*Θ) |
| illuminance | cd/m^2 | L^2*J/L^4 |
| inductance | H | L^2*M/(T^2*I^2) |
| inverse amount | 1/mol | 1/N |
| inverse amount concentration inverse time | m^3/(s*mol) | L^3/(T*N) |
| inverse area | 1/m^2 | 1/L^2 |
| inverse current | 1/A | 1/I |
| inverse length | 1/m | 1/L |
| inverse luminous intensity | 1/cd | 1/J |
| inverse magnetic flux density | s^2*A/kg | T^2*I/M |
| inverse mass | 1/kg | 1/M |
| inverse temperature | 1/K | 1/Θ |
| inverse time | Hz | 1/T |
| inverse time squared | 1/s^2 | 1/T^2 |
| inverse volume | 1/m^3 | 1/L^3 |
| irradiance | kg/s^3 | L^2*M/(L^2*T^3) |
| kinematic viscosity | m^2/s | L^2/T |
| length | m | L |
| length ratio | ° | L/L |
| linear momentum | m*kg/s | L*M/T |
| luminance | cd/m^2 | J/L^2 |
| luminous efficacy | s^3*cd/(m^2*kg) | T^3*J/(L^2*M) |
| luminous energy | s*cd | L^2*T*J/L^2 |
| luminous flux | cd | L^2*J/L^2 |
| luminous flux density | cd/m^2 | L^2*J/L^4 |
| luminous intensity | cd | J |
| luminous intensity ratio | ° | J/J |
| magnetic dipole moment | m^2*A | L^2*I |
| magnetic dipole moment ratio | ° | L^2*I/(L^2*I) |
| magnetic field gradient | kg/(m*s^2*A) | M/(L*T^2*I) |
| magnetic field strength | A/m | I/L |
| magnetic flux | Wb | L^2*M/(T^2*I) |
| magnetic flux density | T | M/(T^2*I) |
| magnetizability | m^2*s^2*A^2/kg | L^2*M*T^4*I^2/(M^2*T^2) |
| mass | kg | M |
| mass concentration | kg/m^3 | M/L^3 |
| mass flow rate | kg/s | M/T |
| mass flux | kg/(m^2*s) | M/(L^2*T) |
| mass ratio | ° | M/M |
| mass to charge ratio | kg/(s*A) | M/(T*I) |
| molality | mol/kg | N/M |
| molar conductivity | s^3*A^2/(kg*mol) | L^2*T^3*I^2/(L^2*M*N) |
| molar energy | m^2*kg/(s^2*mol) | L^2*M/(T^2*N) |
| molar entropy | m^2*kg/(s^2*K*mol) | L^2*M/(T^2*Θ*N) |
| molar heat capacity | m^2*kg/(s^2*K*mol) | L^2*M/(T^2*Θ*N) |
| molar magnetic susceptibility | m^3/mol | L^3/N |
| molar mass | kg/mol | M/N |
| moment of force | J | L^2*M^2/(M*T^2) |
| moment of inertia | m^2*kg | L^2*M |
| permeability | m*kg/(s^2*A^2) | L*M/(T^2*I^2) |
| permittivity | s^4*A^2/(m^3*kg) | T^4*I^2/(L^3*M) |
| plane angle | ° | L/L |
| porosity | ° | L^3/L^3 |
| power | W | L^2*M/T^3 |
| power per luminous flux | m^2*kg/(s^3*cd) | L^3*M/(L*T^3*J) |
| pressure | Pa | M/(L*T^2) |
| pressure gradient | kg/(m^2*s^2) | M/(L^2*T^2) |
| radiance | kg/s^3 | L^4*M/(L^4*T^3) |
| radiant flux | W | L^2*M/T^3 |
| radiant intensity | W | L^4*M/(L^2*T^3) |
| radiation exposure | s*A/kg | T*I/M |
| radioactivity | Hz | 1/T |
| reduced action | m^2*kg/s | L^3*M/(L*T) |
| refractive index | ° | L*T/(L*T) |
| rock permeability | m^2 | L^2 |
| second hyperpolarizability | s^10*A^4/(m^2*kg^3) | L^4*T^10*I^4/(L^6*M^3) |
| second radiation constant | m*K | L^3*M*T^2*Θ/(L^2*M*T^2) |
| solid angle | ° | L^2/L^2 |
| specific energy | m^2/s^2 | L^2/T^2 |
| specific entropy | m^2/(s^2*K) | L^2/(T^2*Θ) |
| specific gravity | ° | L^3*M/(L^3*M) |
| specific heat capacity | m^2/(s^2*K) | L^2/(T^2*Θ) |
| specific power | m^2/s^3 | L^2*M/(M*T^3) |
| specific surface area | m^2/kg | L^2/M |
| specific volume | m^3/kg | L^3/M |
| spectral power | m*kg/s^3 | L^2*M/(L*T^3) |
| spectral radiance | kg/(m*s^3) | L^4*M/(L^5*T^3) |
| spectral radiant energy | N | L^2*M/(L*T^2) |
| spectral radiant flux density | kg/(m*s^3) | M/(L*T^3) |
| spectral radiant intensity | m*kg/s^3 | L^4*M/(L^3*T^3) |
| speed | m/s | L/T |
| stefan-boltzmann constant | kg/(s^3*K^4) | L^2*M/(L^2*T^3*Θ^4) |
| stress | Pa | M/(L*T^2) |
| stress-optic coefficient | m*s^2/kg | L*T^2/M |
| surface area to volume ratio | 1/m | L^2/L^3 |
| surface charge density | s*A/m^2 | T*I/L^2 |
| surface density | kg/m^2 | M/L^2 |
| surface energy | kg/s^2 | L^2*M/(L^2*T^2) |
| surface tension | kg/s^2 | M/T^2 |
| temperature | K | Θ |
| temperature gradient | K/m | Θ/L |
| temperature ratio | ° | Θ/Θ |
| thermal conductance | m^2*kg/(s^3*K) | L^2*M/(T^3*Θ) |
| thermal conductivity | m*kg/(s^3*K) | L*M/(T^3*Θ) |
| time | s | T |
| time ratio | ° | T/T |
| torque | J | L^3*M/(L*T^2) |
| velocity | m/s | L/T |
| voltage | V | L^2*M/(T^3*I) |
| volume | m^3 | L^3 |
| volume per length | m^2 | L^3/L |
| volume power density | kg/(m*s^3) | L^2*M/(L^3*T^3) |
| volume ratio | ° | L^3/L^3 |
| volumetric flow rate | m^3/s | L^3/T |
| wavelength displacement constant | m*K | L*Θ |
| wavenumber | 1/m | 1/L |
As part of the quantities above, CSDM accepts a number of other physical symbols as listed in the table below.
| Name | Symbol | Value in SI units |
|---|---|---|
| acres | ac | 4046.8564224 m^2 |
| alpha particle mass | m_a | 6.64465723e-27 kg |
| amperes | A | 1 A |
| astronomical units | ua | 149597870691 m |
| atmospheres | atm | 101325 kg/(m*s^2) |
| atomic mass constant | m_u | 1.66053904e-27 kg |
| atomic mass units | u | 1.66053904e-27 kg |
| atomic unit of electric field gradient | Λ_0 | 9.717362365265548e+21 m^2*kg/(m^2*s^3*A) |
| atomic unit of energy | E_h | 4.359744651391459e-18 m^2*kg/s^2 |
| atomic unit of length | a_0 | 5.29177210526763e-11 m |
| avogadro constant | N_A | 6.022140857e+23 (1/mol) |
| bars | bar | 100000 kg/(m*s^2) |
| barns | b | 1e-28 m^2 |
| becquerels | Bq | 1 (1/s) |
| bohr magnetons | µ_B | 9.274009992054043e-24 m^2*A |
| boltzmann constant | k_B | 1.38064852e-23 m^2*kg/(s^2*K) |
| brewsters | B | 1e-12 m*s^2/kg |
| british thermal units | Btu | 1055.05585257348 m^2*kg/s^2 |
| calories | cal | 4.1868 m^2*kg/s^2 |
| candelas | cd | 1 cd |
| celsius | °C | 1 K |
| centuries | hyr | 3155760000 s |
| chains | ch | 20.1168 m |
| characteristic impedance of vacuum | Z_0 | 376.7303134803528 m^2*kg/(s^3*A^2) |
| compton wavelengths | λ_C | 2.426310235972943e-12 m |
| conductance quantum | G_0 | 7.748091730820603e-05 s^3*A^2/(m^2*kg) |
| coulombs | C | 1 s*A |
| cups | cup | 0.0002365882365 m^3 |
| curies | Ci | 37000000000 (1/s) |
| daltons | Da | 1.66053904e-27 kg |
| darcys | Dc | 9.869233e-13 m^2 |
| days | d | 86400 s |
| debyes | D | 3.335640951816991e-30 m*s*A |
| decades | dayr | 315576000 s |
| degrees | ° | 0.0174532925199433 m/m |
| drams | dr | 0.0017718451953125 kg |
| dynes | dyn | 1e-05 m*kg/s^2 |
| electric constant | ε_0 | 8.854187817e-12 s^4*A^2/(m^3*kg) |
| electron g factor | g_e | -2.00231930436182 m^2*A/(m^2*A) |
| electron magnetic moment | µ_e | -9.28476462e-24 m^2*A |
| electron mass | m_e | 9.10938356e-31 kg |
| electronvolts | eV | 1.6021766208e-19 m^2*kg/s^2 |
| elementary charge | q_e | 1.6021766208e-19 s*A |
| ergs | erg | 1e-07 m^2*kg/s^2 |
| euler constant | e | 2.71828182845905 |
| fahrenheit | °F | 0.555555555555556 K |
| farads | F | 1 s^4*A^2/(m^2*kg) |
| faraday constant | &F | 96485.33288249877 s*A/mol |
| fathoms | ftm | 1.8288 m |
| fine structure constant | α | 0.00729735256635786 |
| fluid ounces | floz | 2.95735295625e-05 m^3 |
| feet | ft | 0.3048 m |
| furlongs | fur | 201.168 m |
| gallons | gal | 0.003785411784 m^3 |
| gas constant | R | 8.314459861448581 m^2*kg/(s^2*K*mol) |
| gas permeance unit | GPU | 0.33 m*s^2*mol/(m^2*kg*s) |
| gauss | G | 0.0001 kg/(s^2*A) |
| gill | gi | 0.00011829411825 m^3 |
| grains | gr | 6.479891e-05 kg |
| kilograms | kg | 1 kg |
| grams | g | 0.001 kg |
| gravitational constant | &G | 6.67408e-11 m^3/(kg*s^2) |
| gravity acceleration | g_0 | 9.80665 m/s^2 |
| grays | Gy | 1 m^2*kg/(kg*s^2) |
| half teaspoons | halftsp | 2.464460796875e-06 m^3 |
| hectares | ha | 10000 m^2 |
| henries | H | 1 m^2*kg/(s^2*A^2) |
| hertz | Hz | 1 (1/s) |
| horsepower | hp | 745.699872 m^2*kg/s^3 |
| hours | h | 3600 s |
| hundredweight | cwt | 45.359237 kg |
| hundredweightUK | cwtUK | 50.80234544 kg |
| imperial cups | cupUK | 0.000284130625 m^3 |
| imperial fluid ounces | flozUK | 2.84130625e-05 m^3 |
| imperial gallons | galUK | 0.00454609 m^3 |
| imperial gill | giUK | 0.0001420653125 m^3 |
| imperial half teaspoons | halftspUK | 2.959694010416667e-06 m^3 |
| imperial pints | ptUK | 0.00056826125 m^3 |
| imperial quarts | qtUK | 0.0011365225 m^3 |
| imperial quarter teaspoons | quartertspUK | 1.479847005208333e-06 m^3 |
| imperial tablespoons | tbspUK | 1.77581640625e-05 m^3 |
| imperial teaspoons | tspUK | 5.919388020833334e-06 m^3 |
| inches | in | 0.0254 m |
| joules | J | 1 m^2*kg/s^2 |
| katals | kat | 1 mol/s |
| kelvin | K | 1 K |
| kilocalories | kcal | 4186.8 m^2*kg/s^2 |
| kilograms force | kgf | 9.80665 m*kg/s^2 |
| knots | kn | 0.514444444444444 m/s |
| leagues | lea | 4828.032 m |
| light years | ly | 9460730473047448 m |
| links | li | 0.201168 m |
| liters | L | 0.001 m^3 |
| lumens | lm | 1 m^2*cd/m^2 |
| lux | lx | 1 m^2*cd/m^4 |
| magnetic constant | µ_0 | 1.256637061435917e-06 m*kg/(s^2*A^2) |
| magnetic flux quantum | Φ_0 | 2.067832279214686e-15 m^2*kg/(s^2*A) |
| maxwells | Mx | 1e-08 m^2*kg/(s^2*A) |
| meters | m | 1 m |
| miles | mi | 1609.344 m |
| millimeters of Hg | mmHg | 133.322 kg/(m*s^2) |
| minutes | min | 60 s |
| moles | mol | 1 mol |
| moles per liter | M | 1000 mol/m^3 |
| months | month | 2629800 s |
| muon g factor | g_µ | -2.0023318418 m^2*A/(m^2*A) |
| muon magnetic moment | µ_µ | -4.49044826e-26 m^2*A |
| myon mass | m_µ | 1.883531594e-28 kg |
| neutron g factor | g_n | -3.82608545 m^2*A/(m^2*A) |
| neutron magnetic moment | µ_n | -9.662365e-27 m^2*A |
| neutron mass | m_n | 1.674927471e-27 kg |
| newtons | N | 1 m*kg/s^2 |
| nuclear magnetons | µ_N | 5.050783698211084e-27 m^2*A |
| ohms | Ω | 1 m^2*kg/(s^3*A^2) |
| oil barrels | bbl | 0.158987295 m^3 |
| ounces | oz | 0.028349523125 kg |
| ounces force | ozf | 0.2780138509537812 m*kg/s^2 |
| parts per billion | ppb | 1E-09 |
| parts per million | ppm | 1E-06 |
| parts per quadrillion | ppq | 1E-15 |
| parts per ten thousand | ‱ | 0.0001 |
| parts per thousand | ‰ | 0.001 |
| parts per trillion | ppt | 1E-12 |
| pascals | Pa | 1 kg/(m*s^2) |
| percent | % | 0.01 |
| phots | ph | 10000 m^2*cd/m^4 |
| pi | π | 3.141592653589793 m/m |
| pints | pt | 0.000473176473 m^3 |
| planck constant | h_P | 6.62607004e-34 m^2*kg/s |
| planck length | l_P | 1.616228372961306e-35 m |
| planck mass | m_P | 2.176470195687873e-08 kg |
| planck temperature | T_P | 1.416807993922871e+32 K |
| planck time | t_P | 5.391157548338278e-44 s |
| poises | P | 0.1 kg/(m*s) |
| pounds | lb | 0.45359237 kg |
| pounds force | lbf | 4.4482216152605 m*kg/s^2 |
| pounds force per square inch | psi | 6894.75729 kg/(m*s^2) |
| proton g factor | g_p | 5.585694702 m^2*A/(m^2*A) |
| proton magnetic moment | µ_p | 1.4106067873e-26 m^2*A |
| proton mass | m_p | 1.672621898e-27 kg |
| quarts | qt | 0.000946352946 m^3 |
| quarter teaspoons | quartertsp | 1.2322303984375e-06 m^3 |
| radians | rad | 1 m/m |
| rankines | °R | 0.555555555555556 K |
| reduced planck constant | ℏ | 1.054571800139113e-34 m^3*kg/(m*s) |
| rods | rod | 5.0292 m |
| rydbergs | Ry | 2.179872325695729e-18 m^2*kg/s^2 |
| rydberg constant | R_∞ | 10973731.57154738 (1/m) |
| seconds | s | 1 s |
| siemens | S | 1 s^3*A^2/(m^2*kg) |
| sieverts | Sv | 1 m^2*kg/(kg*s^2) |
| speed of light | c_0 | 299792458.0147872 m/s |
| stefan-boltzmann constant | σ | 5.670367e-08 kg/(s^3*K^4) |
| steradians | sr | 1 m^2/m^2 |
| stilbs | sb | 10000 cd/m^2 |
| stokes | St | 0.0001 m^2/s |
| stones | st | 6.35029318 kg |
| tablespoons | tbsp | 1.478676478125e-05 m^3 |
| teaspoons | tsp | 4.92892159375e-06 m^3 |
| tesla | T | 1 kg/(s^2*A) |
| thomson | Th | 1.036426957204542e-08 kg/(s*A) |
| tons | ton | 907.18474 kg |
| tonnes | t | 1000 kg |
| tonsUK | tonUK | 1016.0469088 kg |
| torrs | Torr | 133.3223684210526 kg/(m*s^2) |
| townships | twp | 93239571.972096 m^2 |
| volts | V | 1 m^2*kg/(s^3*A) |
| watts | W | 1 m^2*kg/s^3 |
| webers | Wb | 1 m^2*kg/(s^2*A) |
| weeks | wk | 604800 s |
| wien wavelength displacement constant | b_λ | 0.0028977729 m*K |
| yards | yd | 0.9144 m |
| years | yr | 31557600 s |
| ångströms | Å | 1e-10 m |
| ørsteds | Oe | 79.57747154594767 A/m |