Golden Ruler
Golden Ruler

Planck Units (called "God's Units") are free of anthropocentric arbitrariness

From Wikipedia, the free encyclopedia

Particle Physics


In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants (listed below) in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units have profound significance for theoretical physics since they elegantly simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories such as quantum gravity.


The universal constants that Planck units, by definition, normalize to 1 are:


Gravitational constant, G

Reduced Planck constant, ħ

Speed of light in a vacuum, c

Coulomb constant,(4πε0)−1  (sometimes ke or k)

Boltzmann constant, kB (sometimes k)



Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of the fundamental physical theories and not from interchangeable experimental parameters. Planck units are only one system of natural units among other systems, but are considered unique in that these units are not based on properties of any prototype object or particle (that would be arbitrarily chosen), but rather on properties of free space alone.


The constants can be associated with at least one fundamental physical theory:


G with general relativity and Newtonian gravity,

ħ with quantum mechanics,

c  with electromagnetism and special relativity,

ε0 with electrostatics,

kB with statistical mechanics and thermodynamics.

Dimensionless Quantities 

All systems of measurement feature base units. In the system of Planck units, the Planck base unit of length is known simply as the Planck length, the base unit of time is the Planck time, and so on. These units are derived from the five dimensional universal physical constants  in such a manner that these constants are eliminated from fundamental equations of physical law when physical quantities are expressed in terms of Planck units.

Any ratio of two like-dimensioned quantities is a dimensionless quantity. If, by a shorthand convention, it is axiomatically understood that all physical quantities are expressed in terms of Planck units, ratios may be expressed simply with the symbols of physical quantity, without being scaled by their corresponding unit:




Value in SI units with uncertainties

Speed of light in vacuum


L T −1

2.99792458×108 m s−1

Gravitational constant


L3M−1T −2

6.67384(80)×10−11 m3kg−1s−2

Reduced Planck constant

ħ = h/2π
where h is Planck constant

L2M T −1

1.054571726(47)×10−34 J s

Coulomb constant

whereε0is the permittivity of free space

L3M T −2Q−2

8.9875517873681764×109 kg m3s−2C−2

Boltzmann constant


L2M T −2Θ−1

1.3806488(13)×10−23 J/K

Key: L = length, M = mass, T = time, Q = electric charge, Θ = temperature.   As can be seen above, the gravitational attractive force of two bodies of 1 Planck mass each, set apart by 1 Planck length is 1 Planck force. Likewise, the distance traveled by light during 1 Planck time is 1 Planck length.



Value (SI units)

Planck length

Length (L)

1.616 199(97) × 10−35m

Planck mass

Mass (M)

2.176 51(13) × 10−8kg

Planck time

Time (T)

5.391 06(32) × 10−44s

Planck charge

Electric charge (Q)

1.875 545 956(41) × 10−18C

Planck temperature

Temperature (Θ)

1.416 833(85) × 1032K

Most Planck units are many orders of magnitude too large or too small to be of any practical use, so that Planck units as a system are really      only relevant to theoretical physics. In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding. For example:

A speed of 1 Planck length per Planck time is the speed of light in a vacuum, the maximum possible speed in special relativity; Our understanding of the Big Bang begins with the Planck epoch, when the universe was 1 Planck time old and 1 Planck length in diameter, and had a Planck temperature of 1. At that moment, quantum theory as presently understood becomes applicable.

Understanding the universe when it was less than 1 Planck time old requires a theory of quantum gravity that would incorporate quantum effects into general relativity. Such a theory does not yet exist. At a Planck temperature of 1, all symmetries broken since the early Big Bang would be restored, and the four fundamental forces of contemporary physical theory would become one force. Relative to the Planck Epoch, the universe today looks extreme when expressed in Planck units, as in this set of approximations:

Today's universe in Planck units 

Property of present-day Universe   

Approximate number of Planck units 



8.08 × 1060tP

4.35 × 1017s or 13.8 × 109years


5.4 × 1061lP

8.7 × 1026m or 9.2 × 1010light-years


approx. 1060mP

3 × 1052kg or 1.5 × 1022solar masses


1.9 × 10−32TP

2.725 K

Cosmological constant

5.6 × 10−122tP−2

1.9 × 10−35s−2

Hubble constant

1.24 × 10−61tP−1

67.8 (km/s)/Mpc

Recommend this page on: