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Calculator for Planck Units

Conversion of common physical units into Planck units.

The Planck units form a natural, universal and fundamental system for physical quantities. They were named after Max Planck, the founder of quantum mechanics. These units represent the limits to which we can distinguish cause and effect. Beyond that, our physical laws are no longer applicable. They therefore stand for extreme values, mostly extremely small, sometimes extremely large, often beyond human imagination.

The Planck units can be derived from these natural constants:

Symbol	Natural constant	Meaning	Value
G	Gravitational constant	Strength of gravity	6.6743*10-11 m³/(kg*s²)
c	Speed of Light	Velocity of massless particles (like photons) in vacuum	299792458 m/s
ℎ	Planck constant	Ratio of energy and frequency of a photon	6.62607015*10-34 Js
ℏ	Reduced Planck constant	Ratio of energy and angular frequency of a photon, ℏ=ℎ/(2π)	1.054571817*10-34 Js
kB	Boltzmann constant	Ratio of energy and temperature	1.380649*10-23 J/K
kC	Coulomb constant	Electrostatic ratio	8.987551787*109 Vm/(As)

The basic quantities of the Planck units are:

Symbol	Name	Term	Value
lP	Planck length	√ ℏ G / c³	1.616255*10-35 m
tP	Planck time	√ ℏ G / c5	5.391247-44 s
mP	Planck mass	√ ℏ c / G	2.176434*10-8 kg
TP	Planck temperature	mP c² / kB	1.416764*1032 K
qP	Planck charge	√ ℏ c / kC	1.875545956*10-18 C

Derived quantities of the Planck units are:

Symbol	Name	Term	Value
l²P	Planck area	ℏ G / c³	2.612*10-70 m²
l³P	Planck volume	√ ℏ G / c³ ³	4.222*10-105 m³
EP	Planck energy	mP c²	1.956*109 J

...

The units we are familiar with and use, such as meters, kilograms, seconds and especially degrees Celsius, are chosen arbitrarily. We agreed on them and have become accustomed to them. They are also in the range of what people experience in their environment every day and what they have to deal with. However, if we wanted to use units that result from the fundamental laws of nature and thus from the basis of our existence, then these would be the Planck units. But these units have values ​​that make calculations and visualization complicated and are simply impractical to handle in everyday life as well as in most scientific applications.

Last updated on 06/25/2025. Author: Jürgen Kummer

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