What units can be derived from the constants c, G and h?

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Answer 1 · 2018-01-23T11:16:15

Combinations of c, G and h can yield the squares of mass, time and distance.

Let's look at the three constants in terms of SI units.

The speed of light #c# has units: #m/s#

The gravitational constant #G# has units: #m^3/(kgs^2)#

Planck's constant #h# has units: #(m^2kg)/s#

Let's combines these in different ways:

The square of the unit of length is given by:
#(Gh)/c^3# which has units #m^3/(kgs^2)(m^2kg)/ss^3/m^3=m^2#

The square of the unit of time is given by:
#(Gh)/c^5# which has units #m^3/(kgs^2)(m^2kg)/ss^5/m^5=s^2#

The square of the unit of mass is given by:
#(hc)/G# which has units #(m^2kg)/sm/s(kgs^2)/m^3=kg^2#