Planck length
The Planck length is about 1.616 × 10⁻³⁵ metres, the length you get by combining the gravitational constant, the speed of light and the reduced Planck constant into a quantity with the dimensions of length. It is roughly 10²⁰ times smaller than a proton, and nothing has ever been measured anywhere near it.
Watch out: Physics writes it ℓ_P. The subscript is dropped here because a unit symbol is typeset inside \text{} and an underscore is a parse error. Its numerical value also inherits the uncertainty in G, which is the least precisely known of the fundamental constants, so the digits past the fourth are not solid.
| 1 lP | 1.6162550e-35 m |
Max Planck derived the natural units in 1899 on the argument that a system built only from universal constants carries no arbitrary human choice in it. He had no quantum theory of gravity in mind; the length acquired that significance decades later.