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  • Planck units
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  • The Planck units are a system of units based on five fundamental constants, named after their inventor Max Planck: * The speed of light in a vacuum c, which is equal to exactly 299792458 meters per second * The gravitational constant G, approximately equal to \(6.67408 imes 10^{-11}\) meters cubed per kilogram per second squared * The reduced Planck constant ħ, approximately equal to \(1.05457 imes 10^{-34}\) joule-seconds * The Coulomb constant ke, approximately equal to \(8.98755 imes 10^9\) meters per farad * The Boltzmann constant kB, approximately equal to \(1.380649 imes 10^{-23}\) joules per kelvin
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abstract
  • The Planck units are a system of units based on five fundamental constants, named after their inventor Max Planck: * The speed of light in a vacuum c, which is equal to exactly 299792458 meters per second * The gravitational constant G, approximately equal to \(6.67408 imes 10^{-11}\) meters cubed per kilogram per second squared * The reduced Planck constant ħ, approximately equal to \(1.05457 imes 10^{-34}\) joule-seconds * The Coulomb constant ke, approximately equal to \(8.98755 imes 10^9\) meters per farad * The Boltzmann constant kB, approximately equal to \(1.380649 imes 10^{-23}\) joules per kelvin Below you can see some Planck units: * Planck length \(l_{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616 imes 10^{-35}\) m, * Planck time \(t_{P} = \sqrt{\frac{\hbar G}{c^5}}\approx 5.391 imes 10^{-44}\) s, * Planck mass \(m_{P}=\sqrt{\frac{\hbar c}{G}}\approx 2.176470 imes 10^{-8}\) kg, * Planck energy \(E_{P} = m_{P} c^2 = \frac{\hbar}{t_{P}} = \sqrt{\frac{\hbar c^5}{G}}\approx 10^{19}\)GeV, * Planck temperature \(T_{P} = \frac{m_{P} c^2}{k_B} = \sqrt{\frac{\hbar c^5}{G k_B^2}}\approx 1.416808 imes 10^{32}\) K. By relating these units using dimensional analysis, a system of units can be created. Some Planck units are very small (example: the Planck volume, equal to about \(4.222 imes 10^{-105}\) cubic meters), but some are very large (example: the Planck pressure, equal to about \(4.633 imes 10^{113}\) pascals).