How big is Electron (Classical)? | Scale of the Universe

An electron is a tiny particle with a negative electric charge, found in every atom, outside its nucleus. No experiment has found any size for it: in every test so far, it behaves like a point. The 5.64 femtometers shown above is twice the classical electron radius, a figure from classical, non-quantum physics rather than a measurement. A femtometer is a millionth of a billionth of a meter (10⁻¹⁵ meters).

Size

The classical electron radius is about 2.82 femtometers. It comes from a formula that uses the electron's charge and mass and the speed of light, but nothing from quantum physics. It is roughly the size a ball of the electron's charge would need to be for the energy of its electric field to equal the electron's mass-energy, the energy given by E = mc².

From 1989 to 2000, CERN's Large Electron–Positron collider (LEP) smashed electrons into positrons, particles with the same mass as electrons but the opposite charge. A 2000 analysis of those collisions found no sign that electrons have any size. If an electron has a radius at all, it is less than 2.8 × 10⁻¹⁹ meters, about one ten-thousandth of the classical electron radius. A 2025 paper still gives this as the best limit from such collisions.

Size comparisons

The figure shown, 5.64 femtometers, is about 10,000 times the largest width collision experiments allow an electron, 5.6 × 10⁻¹⁹ meters.
By the classical figure, an electron would be more than three times as wide as a proton, which is about 1.7 femtometers across, even though a proton has 1,836 times the electron's mass.
Going by the experimental limit instead, a proton is at least 3,000 times as wide as an electron.
A helium nucleus, about 3.4 femtometers across, is roughly 6,000 times the largest width allowed for an electron.
If a proton were enlarged to the size of a basketball, an electron on the same scale would be at most 0.08 millimeters across, no wider than a thin human hair.

Why the classical radius is still used

The classical electron radius is not a size, but it is still a useful number. When light or other electromagnetic waves strike a free electron, it scatters them as if it were a small solid ball of about that radius. Physicists use it to work out how strongly electrons scatter this radiation, a process called Thomson scattering.

How the electron was discovered

The British physicist J. J. Thomson identified the electron in 1897, at the Cavendish Laboratory of Cambridge University. He was studying cathode rays, a puzzling kind of ray that travels through glass tubes with almost all the air pumped out. He showed that the rays carried negative charge and could be bent by electric and magnetic fields.

From how far the rays bent, Thomson found that their mass compared with their charge was less than a thousandth of that for a charged hydrogen atom. He proposed that the rays were streams of tiny pieces of atoms, which he called corpuscles. They are now called electrons.