Planck mass unit

data derived with UnitSystems.jl DOI

\[\text{M}\]

\[\left[\text{m}_\text{e}\right]\]

\[m_P = \sqrt{\frac{\hbar c}{G}} = \frac{m_e}{\sqrt{\alpha_G}} = \frac{2R_\infty hg_0}{c\alpha^2\sqrt{\alpha_G}}\]

Quantity Product UnitSystem
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ Metric
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ SI2019
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ SI1976
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\hbar^{-1}\text{R}_\text{K}^{-1}\text{K}_\text{J}^{-2}\text{m}_\text{P}\cdot 2^{2}$ CODATA
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\hbar^{-1}{\text{R}_\text{K}^{90}}^{-1}{\text{K}_\text{J}^{90}}^{-2}\text{m}_\text{P}\cdot 2^{2}$ Conventional
$2.176075(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\Omega_\text{it}\cdot \text{V}_\text{it}^{-2}\text{m}_\text{P}$ International
$2.176021(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}/1.0001900224889804$ InternationalMean
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricTurn
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricSpatian
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricGradian
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricDegree
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricArcminute
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ MetricArcsecond
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ Engineering
$2.219345(24) \times 10^{-9}$ $\left[\text{hyl}\right]$ $\text{g}_0^{-1}\text{m}_\text{P}$ Gravitational
$2.176434(24) \times 10^{-11}$ $\left[\text{t}\right]$ $\text{m}_\text{P}\cdot 2^{-3}5^{-3}$ MTS
$2.176434(24) \times 10^{-5}$ $\left[\text{g}\right]$ $\text{m}_\text{P}\cdot 2^{3}5^{3}$ EMU
$2.176434(24) \times 10^{-5}$ $\left[\text{g}\right]$ $\text{m}_\text{P}\cdot 2^{3}5^{3}$ ESU
$2.176434(24) \times 10^{-5}$ $\left[\text{g}\right]$ $\text{m}_\text{P}\cdot 2^{3}5^{3}$ Gauss
$2.176434(24) \times 10^{-5}$ $\left[\text{g}\right]$ $\text{m}_\text{P}\cdot 2^{3}5^{3}$ LorentzHeaviside
$4.798216(53) \times 10^{-8}$ $\left[\text{lb}\right]$ $\text{lb}^{-1}\text{m}_\text{P}$ FPS
$1.242776(14) \times 10^{-10}$ $\left[\text{slinch}\right]$ $\text{g}_0^{-1}\text{ft}\cdot \text{lb}^{-1}\text{m}_\text{P}\cdot 2^{-2}3^{-1}$ IPS
$1.491331(16) \times 10^{-9}$ $\left[\text{slug}\right]$ $\text{g}_0^{-1}\text{ft}\cdot \text{lb}^{-1}\text{m}_\text{P}$ British
$4.798216(53) \times 10^{-8}$ $\left[\text{lbm}\right]$ $\text{lb}^{-1}\text{m}_\text{P}$ English
$4.798216(53) \times 10^{-8}$ $\left[\text{lbm}\right]$ $\text{lb}^{-1}\text{m}_\text{P}$ Survey
$4.798216(53) \times 10^{-8}$ $\left[\text{lb}\right]$ $\text{lb}^{-1}\text{m}_\text{P}$ MPH
$2.176434(24) \times 10^{-8}$ $\left[\text{kg}\right]$ $\text{m}_\text{P}$ KKH
$2.167007(24) \times 10^{-8}$ $\left[\text{keg}\right]$ $\text{g}_0^{3/2}\text{m}_\text{P}\cdot \text{GM}_\text{E}^{-3/2}\tau^{-3}2^{27}5^{21}$ Nautical
$2.167007(24) \times 10^{-8}$ $\left[\text{keg}\right]$ $\text{g}_0^{3/2}\text{m}_\text{P}\cdot \text{GM}_\text{E}^{-3/2}\tau^{-3}2^{27}5^{21}$ Meridian
$1.094560(12) \times 10^{-38}$ $\left[\text{M}_\odot\right]$ $\hbar\cdot \text{c}\cdot \text{au}^{-3}\text{k}_\text{G}^{-2}\text{m}_\text{P}^{-1}\tau^{-3}2^{28}3^{14}5^{10}$ IAU☉
$3.644296(40) \times 10^{-33}$ $\left[\text{ME}\right]$ $\hbar\cdot \text{c}\cdot \text{m}_\text{P}^{-1}\text{GM}_\text{E}^{-1}\tau^{-1}$ IAUE
$1.146624(13) \times 10^{-35}$ $\left[\text{MJ}\right]$ $\hbar\cdot \text{c}\cdot \text{m}_\text{P}^{-1}\text{GM}_\text{J}^{-1}\tau^{-1}$ IAUJ
$2.389222(26) \times 10^{22}$ $\left[\mathbb{1}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-1}$ Hubble
$8.520(63) \times 10^{-61}$ $\left[\text{M}\right]$ $\hbar\cdot \text{c}^{-2}\Omega_{\Lambda}^{1/2}\text{H}_0\cdot \text{au}^{-1}\text{m}_\text{P}^{-1}\tau^{1/2}2^{-9}3^{-7/2}5^{-6}$ Cosmological
$5.431(20) \times 10^{30}$ $\left[\text{M}\right]$ $\hbar^{-1/2}\text{c}\cdot \Omega_{\Lambda}^{-1/4}\text{H}_0^{-1/2}\text{au}^{1/2}\text{m}_\text{P}^{1/2}\tau^{1/4}2^{11/2}3^{7/4}5^{3}$ CosmologicalQuantum
$3.5449077018110318$ $\left[\text{M}\right]$ $\tau^{1/2}2^{1/2}$ Planck
$1.0$ $\left[\text{m}_\text{P}\right]$ $1$ PlanckGauss
$11.70623761437(90)$ $\left[\text{M}\right]$ $\alpha^{-1/2}$ Stoney
$2.389222(26) \times 10^{22}$ $\left[\mathbb{1}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-1}$ Hartree
$1.194611(13) \times 10^{22}$ $\left[\text{M}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-2}$ Rydberg
$11.70623761437(90)$ $\left[\text{M}\right]$ $\alpha^{-1/2}$ Schrodinger
$2.389222(26) \times 10^{22}$ $\left[\mathbb{1}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-1}$ Electronic
$2.389222(26) \times 10^{22}$ $\left[\mathbb{1}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-1}$ Natural
$2.389222(26) \times 10^{22}$ $\left[\mathbb{1}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\text{m}_\text{P}\cdot 2^{-1}$ NaturalGauss
$1.301211(14) \times 10^{19}$ $\left[\text{m}_\text{p}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\mu_\text{eu}\cdot \mu_\text{pu}^{-1}\text{m}_\text{P}\cdot 2^{-1}$ QCD
$1.301211(14) \times 10^{19}$ $\left[\text{m}_\text{p}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\mu_\text{eu}\cdot \mu_\text{pu}^{-1}\text{m}_\text{P}\cdot 2^{-1}$ QCDGauss
$1.301211(14) \times 10^{19}$ $\left[\text{m}_\text{p}\right]$ $\hbar^{-1}\text{c}\cdot \text{R}_{\infty}^{-1}\alpha^{2}\mu_\text{eu}\cdot \mu_\text{pu}^{-1}\text{m}_\text{P}\cdot 2^{-1}$ QCDoriginal