How big is the Limit of Measured Sizes?

This entry is a marker, not an object. It shows where measured sizes end in the explorer: everything shown smaller than it is a particle with no measured size, or a length that comes from theory rather than measurement. The marker sits at 100 attometers, or 10⁻¹⁶ meters, about a seventeenth of the width of a proton. That figure is approximate and is not itself a measurement.

Size

An attometer is 10⁻¹⁸ meters, a billionth of a billionth of a meter, so 100 attometers is 10⁻¹⁶ meters. The notation 10⁻¹⁶ means 1 divided by a 1 followed by 16 zeros. Immediately above the marker are the smallest objects in the explorer whose sizes have been measured, the neutron and the proton. A proton is about 1.7 femtometers (1.7 × 10⁻¹⁵ meters) across.

The marker's figure is a rough boundary between those measured sizes and the unmeasured ones below. It does not mean that shorter distances are out of reach. Experiments have looked for a size in quarks at distances less than a hundredth of the marker's length, and found none.

Size comparisons

• A proton, about 1.7 femtometers across, is about 17 times as wide as the marker's 100 attometers.
• The marker's length is more than 100 times the largest size experiments allow for a quark, about 8.6 × 10⁻¹⁹ meters across.
• About a million lengths of 100 attometers, laid end to end, would span a hydrogen atom, which is about 0.1 nanometers (a tenth of a billionth of a meter) across.
• If 100 attometers were enlarged to 1 millimeter (0.04 inches), a proton would be about 17 millimeters (0.66 inches) across, and a human hair would be about 1 million kilometers (620,000 miles) wide, about 2.6 times the distance from Earth to the Moon.

How short distances are studied

Physicists study short distances by firing fast particles at a target and watching how they scatter. A moving particle such as an electron also behaves like a wave, and the more energy it has, the shorter its wavelength, the distance from one crest of the wave to the next. A shorter wavelength can reveal finer detail.

In the late 1960s, physicists from SLAC and MIT, in the United States, fired electrons with energies of up to about 20 GeV (billion electronvolts) at protons. At that energy, an electron's wavelength is about 6 × 10⁻¹⁷ meters, a little shorter than the marker's figure and much smaller than a proton. The electrons revealed small, hard grains inside protons, now known to be quarks.

Later experiments looked much closer. At the HERA accelerator, the ZEUS experiment collided electrons with protons and found no sign that quarks have any size. In 2016 it reported that a quark's radius must be less than 4.3 × 10⁻¹⁹ meters.

What lies below the marker

Below the marker, the explorer shows the six kinds of quark, from the up quark to the top quark, a neutrino and a high-energy neutrino. No experiment has measured a size for any of them, so their figures are not measurements. The explorer also shows the range of the weak force, which is estimated from theory.

At the bottom are lengths that come only from theory. The Planck length, 1.6 × 10⁻³⁵ meters, is calculated from three physical constants rather than measured as the size of anything. Superstrings, about 10⁻³⁵ meters in scale, belong to superstring theory, a proposed theory of everything. Such theories are the most speculative and least tested of the attempts to unify the forces of nature.

Sources

• Quarks. In University Physics Volume 3. OpenStax, 2016.
• GUTs: The Unification of Forces. In College Physics, 2nd edition. OpenStax, 2022.
• The Nobel Prize in Physics 1990: Press release. Royal Swedish Academy of Sciences, 1990.
• Limits on the effective quark radius from inclusive ep scattering at HERA. H. Abramowicz et al. (ZEUS Collaboration), Physics Letters B, 2016.
• Summary Tables: Baryons. Particle Data Group, 2025.
• Summary Tables: Quarks. Particle Data Group, 2025.
• The Standard Model. In University Physics Volume 3. OpenStax, 2016.
• SI prefixes. International Bureau of Weights and Measures.
• Proton rms charge radius. NIST CODATA, 2022.
• Bohr radius. NIST CODATA, 2022.
• Planck length. NIST CODATA, 2022.
• Just How Small Is "Nano"?. National Nanotechnology Initiative.
• Moon Fact Sheet. NASA, 2024.