Non-SI Units of the Very Small: Molecules, Atoms, Nuclei, Particles
Turning to the very small, we find non-SI units there also.
The angstrom (Å, A circle) is 10^(-10) m = 0.1 nm, and most elements' atoms have radii within a factor of 2 of an angstrom.
The fermi (fm) is 10^(-15) m, a femtometer, so "fermi" is another name for a SI unit, like "metric ton" or "tonne" for a megagram. It's around the radius of a nucleon; a proton and a neutron.
The barn is 10^(-28) m^2 or 100 fm^2. Reaction cross sections are often expressed in barns, often with SI prefixes.
The atomic mass unit or dalton (Da) is roughly the average mass per nucleon of light elements' atoms, like carbon or oxygen. It is currently defined as 1/12 the mass of a carbon-12 atom. "Dalton" is often given SI prefixes, and masses of biomolecules, like proteins and nucleic acids (DNA, RNA), are often reported in kilodaltons (kDa) or megadaltons (MDa).
The electron volt (eV) is the energy that an electron will gain when dropping through an electric-potential difference of 1 volt. It's not just an electron; it's anything with elementary charge 1, like a proton.
It is often given SI prefixes, and it is often used in atomic, nuclear, and particle physics. With the help of Einstein's famous equation, it is also used as a mass unit. Electrons have mass 511 kiloelectron volts (keV), protons have mass 938.3 megaelectron volts (MeV), (neutrons 939.6 MeV, dalton 931.5 MeV), top quarks have mass 173 gigaelectron volts (GeV), and the Large Hadron Collider can accelerate protons to energies around 6.8 teraelectron volts (TeV).
I am following the usual custom of omitting the Einstein mass-energy factor, (1/c^2).