In physics, the **Planck length**, denoted ℓP, is a unit of length that is the distance light travels in one unit of Planck time. It is equal to 1.616255(18)×10−35 m.^{[1]} It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

# Value

The Planck length ℓP is defined as:

Solving the above will show the approximate equivalent value of this unit with respect to the meter:

The Planck length is about 10−20 times the diameter of a proton.^{[4]} It can be defined using the radius of the hypothesized Planck particle.

# History

In 1899 Max Planck suggested that there existed some fundamental natural units for length, mass, time and energy.^{[5]}^{[6]} These he derived using dimensional analysis, using only the Newton gravitational constant, the speed of light and the "unit of action", which later became the Planck constant. The natural units he further derived became known as the "Planck length", the "Planck mass", the "Planck time" and the "Planck energy".

# Theoretical significance

The Planck length is the scale at which quantum gravitational effects are believed to begin to be apparent, where interactions require a working theory of quantum gravity to be analyzed.^{[7]} The Planck area is the area by which the surface of a spherical black hole increases when the black hole swallows one bit of information.^{[8]} To measure anything the size of Planck length, the photon momentum needs to be very large due to Heisenberg's uncertainty principle and so much energy in such a small space would create a tiny black hole with the diameter of its event horizon equal to a Planck length.

The Planck length is sometimes misconceived as the minimum length of space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry.^{[7]} However, certain theories of loop quantum gravity do attempt to establish a minimum length on the scale of the Planck length, though not necessarily the Planck length itself,^{[7]} or attempt to establish the Planck length as observer-invariant, known as doubly special relativity.

The strings of string theory are modeled to be on the order of the Planck length.^{[7]}^{[13]} In theories of large extra dimensions, the Planck length has no fundamental physical significance, and quantum gravitational effects appear at other scales.