What Are the Charges and Relative Masses of Subatomic Particles?

Every atom is built from three types of subatomic particle: protons carry a positive electric charge of +1, electrons carry a negative charge of −1, and neutrons are electrically neutral. In terms of mass, a proton weighs about 1,836 times more than an electron, and a neutron is just slightly heavier than a proton. Those numbers sound tidy, but the story behind them is far richer than a simple table suggests, touching on everything from the energy that glues quarks together inside a proton to the question of whether these values have stayed constant across the age of the universe.

Charges and Masses of the Three Familiar Particles

Electric charge in everyday atoms comes in whole-number multiples of a single unit, labeled e. A proton carries exactly +1e, an electron carries exactly −1e, and a neutron carries 0. That is why a neutral atom has equal numbers of protons and electrons: their charges cancel perfectly. How perfectly? Experiments have pushed the upper limit on any difference between the proton’s charge and the electron’s charge down to less than about one part in a billion trillion (roughly 10⁻²¹ of the elementary charge).¹ For all practical purposes, those charges are mirror images of each other.

Mass is where things get more interesting. The standard way physicists compare subatomic masses is against the atomic mass unit (u), defined as one-twelfth the mass of a carbon-12 atom. In those units, precision Penning-trap measurements have pinned the electron’s mass at 0.000 548 579 911 u and the proton’s mass at 1.007 276 467 u.² Dividing the proton mass by the electron mass gives the familiar ratio of roughly 1,836 to 1. The neutron sits just above the proton at about 1.008 665 u. In everyday terms, both the proton and neutron each weigh close to one atomic mass unit, while the electron is nearly 2,000 times lighter.

Why the Tiny Neutron-Proton Mass Difference Matters So Much

The neutron is heavier than the proton by only about 0.14% of their average mass.³ That gap corresponds to roughly 1.29 million electron-volts (MeV) of energy. It sounds negligible, but this small difference is one of the reasons the universe contains stable matter at all.

Because the neutron outweighs the proton, a free neutron is unstable. It decays into a proton, an electron, and an antineutrino, releasing energy in the process. Inside a nucleus the story changes: the binding energy from surrounding protons and neutrons can stabilize a neutron, which is why atomic nuclei hold together. If the mass gap ran the other direction and protons were heavier, protons would be the ones that decay, and hydrogen atoms (a single proton plus an electron) could not exist. No hydrogen means no water, no stars burning hydrogen fuel, and no chemistry remotely like what we know. Detailed calculations of the neutron-to-hydrogen-atom mass difference, around 782 keV, help pin down the energy budget of that decay.⁴

Physicists have traced the neutron-proton mass split to a tug-of-war between two effects. One is electromagnetic: the proton, being charged, carries a bit of extra electromagnetic self-energy. The other comes from the slight difference in mass between the two lightest quarks (the up quark and the down quark) that make up protons and neutrons. A recent calculation using the Cottingham formula, which relates electromagnetic contributions to the virtual scattering of photons off the particle, puts the electromagnetic piece at about 0.58 MeV.⁵ The quark-mass difference supplies the rest, tipping the balance so that the neutron ends up heavier. A landmark lattice calculation showed that both effects can be computed from first principles and together reproduce the measured 1.29 MeV gap.³

Where Most of a Nucleon’s Mass Actually Comes From

If you add up the bare masses of the quarks inside a proton (two up quarks and one down quark), you get only about 1% of the proton’s total mass. The rest, the overwhelming majority, comes from the energy of the strong force that binds those quarks together. This is the domain of quantum chromodynamics (QCD), the part of the Standard Model that describes the strong interaction. The energy stored in gluon fields and in the kinetic motion of quarks trapped at close range is what gives the proton and neutron their heft.⁶

This is a genuinely strange situation. You might expect that the mass of a composite thing is just the sum of the masses of its parts. For a bag of marbles, that works fine. For a proton, it is wildly wrong. Einstein’s equivalence of energy and mass means all that binding energy registers as mass. So when you step on a bathroom scale, the vast bulk of what the scale reads comes not from the intrinsic mass of quarks or electrons but from the strong-force energy inside every proton and neutron in your body.

The Higgs field, often credited in popular accounts as “giving particles their mass,” is responsible for the intrinsic masses of quarks and electrons. But because those intrinsic quark masses contribute so little to the overall nucleon mass, the Higgs mechanism accounts for only a small slice of the mass you encounter in daily life. The heavy lifting, paradoxically, is done by the energy of massless gluons bouncing around inside nucleons.

Quarks and Their Fractional Charges

Protons and neutrons are not truly elementary; they are made of quarks held together by gluons. Up quarks carry a charge of +2/3 e, and down quarks carry −1/3 e. A proton (two ups and one down) works out to +1, and a neutron (two downs and one up) works out to 0. There are six flavors of quark in total, arranged in three pairs of increasing mass: up and down, charm and strange, top and bottom. The top quark is the heaviest known elementary particle, roughly 175 times the mass of a proton.

Quarks never appear in isolation under normal conditions. The strong force gets stronger with distance rather than weaker, so pulling two quarks apart eventually requires enough energy to create a new quark-antiquark pair. This property, called confinement, means you only ever see quarks bundled into composite particles such as protons, neutrons, and short-lived exotics. The experiments that established the extreme neutrality of bulk matter confirmed that isolated quarks are not rattling around inside ordinary steel: fewer than one free quark per roughly two sextillion nucleons.¹

Electrons, Muons, Taus, and Neutrinos

On the other side of the particle family tree sit the leptons, which are not made of quarks and do not feel the strong force. The electron is the lightest and most familiar. Its heavier cousins, the muon (about 207 times the electron mass) and the tau (about 3,477 times the electron mass), behave like overweight electrons: same charge, same interactions, just more massive and less stable. Understanding why these three leptons have such dramatically different masses remains an open question. Theoretical models have explored the idea that only the tau acquires its mass directly through the standard Higgs mechanism, while the lighter electron and muon masses arise through more indirect, loop-level processes.⁷

Each charged lepton has a paired neutrino: the electron neutrino, muon neutrino, and tau neutrino. Neutrinos carry zero electric charge. For decades they were assumed to be massless, but experiments in the late 1990s and early 2000s showed they do have tiny masses, at least a million times smaller than the electron mass. The exact values are still being pinned down. Intriguingly, within the Standard Model, neutrinos could in principle carry a minuscule electric charge if the symmetry structure of the theory were extended slightly. Theoretical work has shown that only certain symmetry extensions, specifically those that shift all lepton flavors equally rather than treating each flavor differently, remain consistent with what neutrino oscillation experiments actually observe.⁸ Any such charge would be extraordinarily small, and there is no experimental evidence it exists.

How These Values Are Measured

The workhorse for modern precision mass measurements is the Penning trap, a device that uses strong magnetic and electric fields to confine a single charged particle. By measuring how fast the trapped particle orbits (its cyclotron frequency), physicists can extract the charge-to-mass ratio to astonishing precision. Recent Penning-trap campaigns have nailed the mass of helium-3 to 12 parts per trillion.⁹ The helium-4 mass has been pinned down to a similar level of precision.¹⁰

These are not just academic exercises. The precision matters because nuclear masses encode information about binding energies, reaction thresholds, and fundamental constants. When the electron mass was measured at better than one part per billion, it simultaneously improved the value of the proton mass and the proton-to-electron mass ratio.² Every digit of improvement feeds into calculations across physics, from tests of quantum electrodynamics to the interpretation of astrophysical spectra.

Charge measurements rely on a different strategy. Because electric charge always appears in exact multiples of e (aside from quarks, which are confined), testing charge equality between protons and electrons comes down to checking whether bulk matter is truly neutral. The most sensitive such tests pass beams of atoms through electric fields and look for any deflection. The absence of deflection down to extraordinary sensitivity is what gives the sub-10⁻²¹ bound on any proton-electron charge asymmetry.¹

Antimatter Has Matching Numbers

Every particle in the Standard Model has an antimatter counterpart with the same mass but opposite charge. The positron (anti-electron) carries +1e, the antiproton carries −1e, and the antineutron is neutral (though its internal quark charges are flipped). A fundamental symmetry called CPT invariance predicts that particle and antiparticle should have exactly the same mass. If they did not, it would signal a crack in the foundations of modern physics.

Experimentalists have tested this to stunning precision. Measurements at CERN’s BASE experiment compared the charge-to-mass ratios of the proton and antiproton and found them equal to within 16 parts per trillion.¹¹ Laser spectroscopy of an exotic atom in which an antiproton replaces an electron around a helium nucleus has independently confirmed the antiproton-to-electron mass ratio at 1836.152674, consistent with the known proton-to-electron ratio.¹² So far, no experiment has found any difference between a particle’s mass and its antiparticle’s mass.

Have These Values Always Been the Same?

One way to check whether fundamental constants are truly constant is to compare present-day laboratory values with values imprinted on light that has traveled billions of years. Molecular hydrogen in distant gas clouds absorbs light at wavelengths that depend sensitively on the proton-to-electron mass ratio. If that ratio were different billions of years ago, the absorption lines would shift in a characteristic pattern.

An early analysis of hydrogen absorption in two quasar sightlines reported a possible change in the mass ratio of roughly two parts in a hundred thousand over the past 12 billion years.¹³ That result caused excitement because even a small drift in such a basic ratio would demand new physics. However, later observations using more absorption lines from a different quasar found a result consistent with zero change, constraining any variation to less than a few parts per million.¹⁴

Laboratory clocks provide an independent check over shorter timescales. By comparing the frequency of a molecular vibration in sulfur hexafluoride with the cesium atomic clock over time, one experiment placed a limit on any drift in the proton-to-electron mass ratio of less than a few parts in 10¹⁴ per year, consistent with no change at all.¹⁵ The current consensus is that the ratio has been constant, or very nearly so, across the observable history of the universe. The earlier quasar hint has not held up against more precise data.

Could Dark Matter Carry a Tiny Charge?

The Standard Model particles described above account for only about 5% of the universe’s energy content. The rest includes dark energy and dark matter, neither of which fits neatly into the proton-neutron-electron picture. One speculative idea is that dark matter particles carry a very small electric charge, a fraction of e far too tiny to have been noticed in particle detectors but potentially large enough to leave astrophysical footprints.

These hypothetical “millicharged” particles would interact weakly with magnetic fields and could form a kind of diffuse plasma. Researchers have used observations of galaxy-cluster collisions, like the famous Bullet Cluster, to set limits on how large such a charge could be. If millicharged dark matter existed with too high a charge for its mass, the two dark-matter halos would have slowed each other down noticeably during the collision, and they did not.¹⁶ Other constraints come from Earth’s own magnetic field: if lightweight millicharged dark matter particles were streaming through the planet, they would interact with the geomagnetic field in ways that sensitive magnetometer networks could detect. Null results from those searches have pushed upper bounds on the charge of very light bosonic dark matter candidates down dramatically.¹⁷

None of these searches have found evidence that dark matter is electrically charged. The constraints are tight enough that if dark matter does carry any charge, it must be extraordinarily small relative to the charges of known particles. Still, the question remains open, and each new generation of experiments carves out a little more of the parameter space where millicharged dark matter could hide.

A Quick Reference for the Numbers

Because the numbers scattered through this article serve different contexts, here they are gathered in one place for easy comparison:

Proton: charge +1e, mass ≈ 1.007 u, about 1,836 times the electron mass
Neutron: charge 0, mass ≈ 1.009 u, about 1,839 times the electron mass (roughly 0.14% heavier than the proton)
Electron: charge −1e, mass ≈ 0.000549 u, the lightest of the three by far
Up quark: charge +2/3 e, bare mass roughly 2 MeV (a tiny fraction of the proton it helps form)
Down quark: charge −1/3 e, bare mass roughly 5 MeV
Muon: charge −1e, mass about 207 times the electron mass
Tau: charge −1e, mass about 3,477 times the electron mass
Neutrinos: charge 0, mass nonzero but at least a million times lighter than the electron

Antiparticles mirror these values: same mass, opposite charge. Every experimental test so far has confirmed that symmetry to extraordinary precision, with the best proton-antiproton comparison agreeing to 16 parts per trillion.¹¹

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