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natural.units
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# This file is the units database in the Natural Units convention
# for use with GNU units by Adrian Mariano <[email protected]>.
#
# 10 Apr 2015 Version 0.10 by Sho Iwamoto
# 01 Jun 2019 Version 0.20 by Sho Iwamoto
# - transit to 2019 new SI definition
# - experimental values from CODATA2018 + PDG2018/2019
# - rename "atomic mass unit" to "unified atomic mass unit"
# 04 Jun 2020 Version 0.21 by Sho Iwamoto
# - accept PDG2020 values
# 16 Jun 2022 Version 0.22 by Sho Iwamoto
# - accept PDG2022 values
#
###########################################################################
# Fundamental units and values #
###########################################################################
GeV !
eV 1e-9 GeV
electronvolt eV
pi 3.14159265358979323846
c 299792458 m/s # exact (defining); should be 1
h 6.62607015e-34 J/Hz # exact (defining); should be 2pi
e 1.602176634e-19 C # exact (defining)
avogadro 6.02214076e23 /mol # exact (defining)
kB 1.380649e-23 J/K # exact (defining); should be 1
hbar h / 2 / pi # should be 1
mu0 1.25663706212e-6 N/A^2 # CODATA2018
epsilon0 1/mu0 c^2 # derived
joule 1|1.602176634e-19 eV # exact; because eV = e V.
# cf. eV/J = (V e) / (V C) = e/C.
A sqrt(1.25663706212e-6 N) # experimentally defined; because mu0 = 1
s 2pi / (6.62607015e-34 J) # exact; because h = 2pi
m 1 / (299792458 /s) # exact; because c = 1
K 1.380649e-23 J # exact; because kB = 1
g 1e-3 J / (m^2/s^2) # exact
mol !
cd !
rad !dimensionless
sr !dimensionless
N_A avogadro
J joule
###########################################################################
# SI units #
###########################################################################
second s
sec s
meter m
gram g
ampere A
kelvin K
mole mol
candela cd
radian rad
steradian sr
hertz /s
newton J/m
pascal N/m^2
watt J/s
coulomb A s
volt W/A
farad C/V
ohm V/A
siemens A/V
weber V s
tesla Wb/m^2
henry Wb/A
# lumen cd sr
# lux lm/m^2
# beqcuerel /s
# gray m^2/s^2
# sievert m^2/s^2
# katal mol/s
N newton
Pa pascal
W watt
C coulomb
V volt
S siemens
F farad
Wb weber
H henry
T tesla
Hz hertz
# lm lumen
# lx lux
# Bq beqcuerel
# Gy gray
# Sv sievert
# kat katal
###########################################################################
# SI Prefixes (longer names must come first) #
###########################################################################
quetta- 1e30
ronna- 1e27
yotta- 1e24
zetta- 1e21
exa- 1e18
peta- 1e15
tera- 1e12
giga- 1e9
mega- 1e6
myria- 1e4
kilo- 1e3
hecto- 1e2
deca- 1e1
deka- deca
deci- 1e-1
centi- 1e-2
milli- 1e-3
micro- 1e-6
nano- 1e-9
pico- 1e-12
femto- 1e-15
atto- 1e-18
zepto- 1e-21
yocto- 1e-24
ronto- 1e-27
quecto- 1e-30
Q- quetta
R- ronna
Y- yotta
Z- zetta
E- exa
P- peta
T- tera
G- giga
M- mega
k- kilo
h- hecto
da- deka
d- deci
c- centi
m- milli
u- micro # it should be "mu" but "u" is easy to type
n- nano
p- pico
f- femto
a- atto
z- zepto
y- yocto
r- ronto
q- quecto
###########################################################################
# Other traditional units (not recommended to use) #
###########################################################################
percent 0.01
% percent
ppm 1e-6
ppb 1e-9
ppt 1e-12
inch 0.0254 m # definition
in inch
gauss 1e-4 tesla
G gauss
angstrom 1e-10 m
dyne 1e-5 newton
erg 1e-7 joule
barn 1e-28 m^2
b barn
thermochemicalcalorie 4.184 J # definition
calorie thermochemicalcalorie
cal thermochemicalcalorie
atmosphere 101325 Pa # definition
atm atmosphere
Torr 1|760 atmosphere # definition
circle 2 pi radian
degree 1|360 circle
deg degree
arcdeg degree
arcmin 1|60 degree
arcminute arcmin
' arcmin
arcsec 1|60 arcmin
arcsecond arcsec
" arcsec
minute 60 s
min minute
hour 60 min
hr hour
day 24 hr
d day
week 7 day
wk week
###########################################################################
# Other units and constants for astrophysics and cosmology #
###########################################################################
G_N 6.70883e-39 / GeV^2 # CODATA2018
planckmass 1/sqrt(G_N)
reducedplanckmass planckmass / sqrt(8 pi)
M_pl planckmass
M0 reducedplanckmass
fermiconstant 1.1663788e-5/GeV^2 # PDG2022
G_F fermiconstant
unifiedatomicmassunit 931.49410242 MeV/c^2 # CODATA2018
u unifiedatomicmassunit
dalton unifiedatomicmassunit
Da dalton
tropicalyear 31556925.1 sec # [of 2020] PDG2022
siderealyear 31558149.8 sec # [of 2020] PDG2022
year tropicalyear
yr year
lightyear 365.25 day c # depricated; NIST publication 811
ly lightyear
astronomicalunit 149597870700 m # definition
au astronomicalunit
parsec 3.08567758149e16 m # definition
pc parsec
solarmass 1.98841e30 kg # PDG2022
earthmass 5.97217e24 kg # PDG2022
presentcmbtemperature 2.7255 K # PDG2022
T_CMB presentcmbtemperature
presenthubbleconstant 100 0.674 km/s/Mpc # PDG2022
H0 presenthubbleconstant
criticaldensity 3H0^2 / (8pi G_N)
rho_crit criticaldensity
###########################################################################
# Other units and constants for particle physics #
###########################################################################
###########################################################################
# Particle masses and widths (from PDG2022) #
###########################################################################
mass_electron 0.51099895000 MeV
mass_muon 105.6583755 MeV
mass_taulepton 1776.86 MeV
mass_charmquark 1.27 GeV
mass_bottomquark 4.18 GeV
mass_topquark 172.69 GeV # based on direct measurement
mass_Wboson 80.377 GeV
mass_Zboson 91.1876 GeV
mass_higgsboson 125.25 GeV
mass_proton 938.27208816 MeV
mass_neutron 939.56542052 MeV
mass_chargedpion 139.57039 MeV
mass_neutralpion 134.9768 MeV
mass_chargedkaon 493.677 MeV
mass_neutralkaon 497.611 MeV
width_muon 1/(2.1969811e-6 s)
width_taulepton 1/(290.3e-15 s)
width_topquark 1.42 GeV
width_Wboson 2.085 GeV
width_Zboson 2.4952 GeV
width_higgsboson 3.2 MeV # ongoing measured; large uncertainty
width_neutron 1/(878.4 s)
width_chargedpion 1/(2.6033e-8 s)
width_neutralpion 1/(8.43e-17 s)
width_chargedkaon 1/(1.2380e-8 s)
width_neutralkaonshort 1/(0.8954e-10 s)
width_neutralkaonlong 1/(5.116e-8 s)
m_e mass_electron
m_mu mass_muon
m_tau mass_taulepton
m_c mass_charmquark
m_b mass_bottomquark
m_t mass_topquark
m_W mass_Wboson
m_Z mass_Zboson
m_H mass_higgsboson
m_p mass_proton
m_n mass_neutron
m_pi mass_chargedpion
m_pi0 mass_neutralpion
m_K mass_chargedkaon
m_K0 mass_neutralkaon
gamma_mu width_muon
gamma_tau width_taulepton
gamma_t width_topquark
gamma_W width_Wboson
gamma_Z width_Zboson
# gamma_H width_higgsboson
gamma_n width_neutron
gamma_pi width_chargedpion
gamma_pi0 width_neutralpion
gamma_K width_chargedkaon
gamma_KS width_neutralkaonshort
gamma_KL width_neutralkaonlong