# 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 $$6.67408 \times 10^{-11}$$ meters cubed per kilogram per second squared
• The reduced Planck constant ħ, approximately equal to $$1.05457 \times 10^{-34}$$ joule-seconds
• The Coulomb constant ke, approximately equal to $$8.98755 \times 10^9$$ meters per farad
• The Boltzmann constant kB, approximately equal to $$1.380649 \times 10^{-23}$$ joules per kelvin

Below you can see some Planck units:

• Planck length $$l_{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616 \times 10^{-35}$$ m,
• Planck time $$t_{P} = \sqrt{\frac{\hbar G}{c^5}}\approx 5.391 \times 10^{-44}$$ s,
• Planck mass $$m_{P}=\sqrt{\frac{\hbar c}{G}}\approx 2.176470 \times 10^{-8}$$ 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 $$T_{P} = \frac{m_{P} c^2}{k_B} = \sqrt{\frac{\hbar c^5}{G k_B^2}}\approx 1.416808 \times 10^{32}$$ 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 $$4.222 \times 10^{-105}$$ cubic meters), but some are very large (example: the Planck pressure, equal to about $$4.633 \times 10^{113}$$ pascals).[1]

## Sources Edit

1. https://en.wikipedia.org/wiki/Planck_units
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