How big is Planck Length? | Scale of the Universe

The Planck length is a unit of length built from three constants of nature, and it is about 1.6 × 10⁻³⁵ meters. That number is 1.6 divided by a 1 followed by 35 zeros. The Planck length is defined, not measured, and it lies far below the smallest distances any experiment can probe. Physicists expect the quantum effects of gravity to become important at around this scale.

Definition

The Planck length combines three constants: the speed of light, c; the gravitational constant, G, which sets the strength of gravity; and the reduced Planck constant, ħ, which sets the scale of quantum effects. It equals the square root of ħG/c³. The internationally recommended value, published by the U.S. National Institute of Standards and Technology (NIST), is 1.616255 × 10⁻³⁵ meters.

The last two digits of that value are uncertain. The speed of light and the reduced Planck constant have exact values by definition, but the gravitational constant is known only to about 2 parts in 100,000. The explorer shows the Planck length as 0.000000000016 yoctometers, where a yoctometer is 10⁻²⁴ meters. Even the smallest unit with an official metric prefix, the quectometer (10⁻³⁰ meters, added in 2022), is about 62,000 Planck lengths.

Size comparisons

A proton, about 1.7 femtometers (1.7 × 10⁻¹⁵ meters) across, is about 100 billion billion (10²⁰) Planck lengths wide. In the explorer, the quarks and the neutrino that sit between the proton and the Planck length show figures that are not measurements.
Experiments at the HERA particle collider found that quarks are less than 8.6 × 10⁻¹⁹ meters across. That limit is still about 50 million billion (5 × 10¹⁶) Planck lengths.
If a Planck length were enlarged to the width of a human hair, about 0.1 millimeters, a proton would be about a light-year across. A light-year is the distance light travels in one year.
If a hydrogen atom, about 0.1 nanometers across, were enlarged to the width of the observable universe, about 93 billion light-years, a Planck length would be about 130 meters (430 feet) long. That is a little longer than an American football field.

Planck's natural units

The German physicist Max Planck proposed the unit in 1899, in a paper to the Prussian Academy of Sciences in Berlin. He pointed out that the usual units of length and time came from the size and motion of Earth. He wanted units of length, mass, time and temperature that would keep their meaning at all times, even for civilizations beyond Earth. So he built them from constants of nature.

Planck's own figure was 4.13 × 10⁻³³ centimeters, about 2.6 times today's value. Most of the difference comes from the constant he used. Today's definition uses the reduced Planck constant, which is Planck's constant divided by 2π, and that alone makes the length about two-fifths of Planck's. More precise measurements of the constants account for the rest.

A smallest length

At the Planck length, both general relativity (the theory of gravity) and quantum mechanics would matter. Many approaches to a theory of quantum gravity suggest that nature has a smallest meaningful length, near the Planck length. This is theory, not measurement, and physicists still debate what form such a limit would take, or whether one exists.

A matching unit of time is the Planck time, about 5.4 × 10⁻⁴⁴ seconds. It is the time light takes to cross one Planck length.