Planck Mass


The Planck mass is a fundamental classical constant, setting the baseline for the unit of mass.  In the section on spacetime, the Planck units are described as the components of spacetime itself, referred to as granules, which can be modeled classically as a spring-mass system to derive fundamental physical constants where only five fundamental constants are required.  The following figure describes the relationship of four of these Planck constants.    

Planck constants describe the structure of spacetime

Unit Cell of Spacetime Lattice


Planck mass is the mass of a single granule.  Although it is a large mass for a small component of space – a granule has a radius of Planck length – its energy/mass is only recognized when it is in motion, consistent with the mechanics of a spring-mass system.

Planck mass - mass of a granule

Planck Mass – Radius of a Granule


See also: Planck time, Planck length, Planck charge



Derivation – Planck Mass

In classical constant format, the Planck time is one of the five fundamental physical constants that most other constants can be derived. It is set here to the magnetic constant (μ0), which is not one of the five fundamental constants, to establish its value. When expressed with this term, it is the one-dimensional displacement from equilibrium (Planck charge) squared over the radius of a granule (Planck length).  The Coulomb constant page describes similarities of this mass to other energy/mass equations.

The wave constant form is derived directly from the classical form.


Classical Constant Form

Planck Mass Derived

Wave Constant Form

Planck Mass Derived Wave Equations

Using classical constants Using energy wave constants


Calculated Value: 2.1765E-08
Difference from CODATA: 0.000%
Calculated Units: kg
G-Factor: gλ-2


Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.