What is Planck’s constant?

Planck’s constant is the famous constant of proportionality discovered by Max Planck at the end of the 19th century. The constant is instrumental in calculating physical quantities on tiny scales including the properties of elementary particles.

Calculating a particle’s wavelength, momentum, and energy is simple. Multiply Planck’s constant by the right inputs and out comes the answer. For well over a century, the constant has improved our understanding of the quantum universe. But is there more to Planck’s constant than simply producing the right answers? Does the quantity 6.626 x 10-34 kgm2/s have deeper meaning?

The answer lies in the elementary form of the constant. Planck’s constant is made up of Planck units which are natural quantities of length, mass, and time.

Planck length
Planck length
Planck mass
Planck mass
Planck time
Planck time

Planck’s constant has four unitsβ€”two units of length, one unit of mass, and one unit of time. These units are arranged into useful ratios for calculating the mechanical properties of elementary particles and systems.

We can show the reduced Planck constant using only the elementary Planck units, or we can simplify the constant using 𝑐 for the speed of light.

elementary form

Planck's constant, Planck length squared Planck mass divided by Planck time

simple form

Planck's constant, Planck length, Planck mass, speed of light

The defining characteristic of Planck’s constant is the ratio π‘™π‘ƒπ‘šπ‘ƒ/𝑑𝑃—the Planck momentum. Multiplying the constant by 𝑐 produces the Planck energy. The remaining quantity 𝑙𝑃 in the numerator pairs up with a particle’s wavelength in the denominator to create a dimensionless operator.

Wavelength operator, ratio of Planck length to de Broglie wavelength
The dimensionless wavelength operator

In formulas with Planck’s constant, it is really the Planck units doing the heavy lifting. This is evident in the granular structure of these formulas.


The traditional formula for momentum uses Planck’s constant in the numerator and a particle’s wavelength in the denominator. Replacing Planck’s constant with natural units of length, mass, and time produces a formula

The natural formula for momentum in fundamental Planck units

The natural form of the equation has two parts:

  1. The maximum potential of the unit dimensions we are solving forβ€”in this case, momentum. The product of Planck mass and the speed of light creates the maximum momentum potential.
  2. A dimensionless proportionality operator in the ratio of Planck length to the particle’s wavelength. This dimensionless ratio reduces the maximum momentum potential in the right proportion.

The following illustration emphasizes the two distinct parts of each natural formula.

The natural formula for momentum shown as a dimensionless proportionality operator and maximum momentum potential

Photon Energy

The formula for photon energy includes another quantity of 𝑐 in the numerator, creating the Planck energy potential on the right and the same ratio of Planck length to particle wavelength on the left.

The natural formula for photon energy in fundamental Planck units

We can think of the photon’s wavelength as diluting the Planck energy, with longer wavelengths generating less energy and shorter wavelengths producing more. A photon reaches the maximum energy limit when its wavelength is equal to the Planck length.


Planck’s constant can also calculate a particle’s wavelength. For massive particles, the formula uses inputs of rest mass π‘š0 and velocity 𝑣 in the denominator to find the particle’s de Broglie wavelength. Each input pairs up with its maximum potential to create a dimensionless operator.

The natural formula for de Broglie wavelength in fundamental Planck units

Multiplying the Planck length by the inverse operators produces the particle’s wavelength. The formula also works for particles moving at the speed of light when velocity is 𝑐.

The natural formula for Compton wavelength in fundamental Planck units

The second wavelength formula gives a particle’s Compton wavelength.

Replacing Planck’s constant with elementary Planck units reveals hidden information about the natural world that is explained by the New Foundation Model of physics. This model gives new meaning to abstract mathematical ideas and explains traditional formulas in terms of the physical unit dimensions length, mass, and time.

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