If the nucleus is up to 100,000 times smaller than its atom, why does it carry almost all the weight?
Because size and mass are not the same property, and the atomic nucleus is where they separate most violently. A nucleus roughly one femtometer wide holds more than 99.9 percent of its atom’s mass, at a density near 1017 kilograms per cubic meter. One teaspoon of that material would weigh about 500 million metric tons. What stops it from blowing itself apart is a force around a hundred times stronger than electromagnetism, and that force reaches almost nowhere.
A pea at the center of a stadium
Measured across, a nucleus is about one femtometer, or 10−15 meters, while the atom around it spans roughly 10−10 meters. That ratio makes the nucleus 10,000 to 100,000 times smaller than the electron cloud giving the atom its size. Numbers on that scale slide off the brain, so let’s make them physical.
Picture a soccer stadium 100 meters across. If the stadium were the atom, the nucleus sitting at midfield would be a pea. Prefer architecture? The ratio between nucleus and atom matches the ratio between the head of a pin and the entire dome of St. Peter’s Basilica in Rome, roughly 42 meters of Renaissance stone hanging over a speck of metal.
Nearly all of an atom’s volume is empty space. Squeeze together the nuclei of every atom in a human body with no gaps left between them, and the result fits inside a grain of salt while still weighing exactly what you weigh.
We ran that one. A 70-kilogram person at 1017 kilograms per cubic meter occupies 7 × 10−16 cubic meters, which works out to a cube about 8.9 micrometers on a side. The grain of salt turns out to be generous by a factor of thirty in width and forty thousand in volume. You would be looking at a speck the size of a single red blood cell.
By volume, you are almost entirely nothing.
Half a billion tons in a teaspoon
Nuclear matter sits near 1017 kilograms per cubic meter, a figure so far outside daily experience that comparison is the only way in. The classic line says a teaspoon of it would weigh as much as a mountain. That claim gets repeated constantly without anyone checking it. So we checked.
A teaspoon holds 5 milliliters, which is 5 × 10−6 cubic meters, and multiplying by 1017 gives 5 × 1011 kilograms, or about 500 million metric tons.
Popular articles round this up to a billion tons. Taking the higher densities found deeper inside heavy nuclei gets you there, and that is a defensible move. Most of the pages quoting the billion-ton figure never say which density they used, though, and several print 1017 in the same paragraph without noticing the contradiction. We would rather show you the arithmetic than hand you the roundest available number.
One caveat we can’t remove. Nuclear density isn’t a single number the way the speed of light is a single number, since it varies from nucleus to nucleus and with depth inside a heavy one, and our source for this piece is a reference dossier rather than a specific measurement paper. Treat 1017 as the right order of magnitude, and treat any figure quoted to two decimal places with suspicion.
Your mass is mostly energy
Protons and neutrons are not elementary particles; each one is built from quarks bound together by gluons. The masses of those quarks account for only a tiny fraction of a proton’s mass.
Nearly all the rest comes from the kinetic energy of the quarks and the binding energy of the gluon field, converted into mass through Einstein’s equivalence of mass and energy. Read that again slowly. When you step on a scale, the number you see is almost entirely trapped energy. We think that is one of the most beautiful facts in physics, and we will say so without hedging.
Why the four forces sit at the strengths they do is a separate question. We took it up in our guide to the fundamental forces and the anthropic principle. That piece works through how narrow the window was: shift the strong interaction by two percent and the early universe converts all its hydrogen into helium, leaving no water anywhere.
We are leaving quark confinement out of this article. Why a single quark can never be pulled free of a proton is a real question with a long answer, and it deserves its own piece rather than a paragraph here.
What keeps the protons from flying apart?
The strong nuclear force does, and it earns the name. Every proton carries positive charge, so electromagnetism shoves them apart hard at femtometer distances. Somehow the nucleus survives anyway.
Strength is roughly 100 times that of electromagnetism, which sounds like more than enough. It comes with a catch. The strong force acts only across distances comparable to the diameter of the nucleus itself, so stretch two nucleons a few femtometers apart and the grip is simply gone. Beyond that range, electromagnetism wins.
That short leash has consequences far outside the nucleus. Nuclear fusion needs the crushing pressure of a stellar core precisely because nucleons must be forced within a few femtometers of each other before the strong force can act, a story we work through in our comparison of nuclear fusion and fission, where the Sun manages at 15 million degrees while a reactor on Earth needs ten times that.
Not every atomic nucleus is a sphere
Many nuclei, particularly those with an odd number of protons or neutrons, are nothing like spheres.
- Spherical, the textbook case.
- Prolate, stretched along one axis like a rugby ball.
- Pear-shaped, bulging asymmetrically so that one end of the nucleus differs from the other.
- Halo nuclei, heavy and neutron-rich, where the protons stay in the center while surplus neutrons drift outward into an outer shell of nearly pure neutron matter.
Shape isn’t fixed either. A nucleus that absorbs energy and becomes excited can swell, deform, or spin at dizzying rates before settling down and shedding the excess as gamma rays. Stretch the neutron shell of a halo nucleus far enough and its effective radius runs well past the one-femtometer scale governing everything else in this article.
Our dossier names the shapes without naming the isotopes. So we can’t tell you which halo nucleus was characterized first, or how thick its neutron skin runs, and we would rather admit that than pad the section with numbers we haven’t checked.
What makes a nucleus magic?
Certain counts of protons or neutrons, among them 2, 8, 20, 50 and 82, give a nucleus exceptional stability. The effect mirrors chemistry almost exactly. Atoms with complete electron shells, the noble gases, barely react with anything, and nuclei with complete nucleon shells show the same aloofness.
This is more than bookkeeping. Laboratories are racing to build artificial superheavy elements, and theory predicts that past a certain mass there should be an island of stability, a region where extremely heavy nuclei stop decaying in fractions of a second and persist instead for minutes or hours. Nobody has planted a flag there yet. We think someone will within our lifetimes, and the magic numbers are the map.
A nucleus the size of a city
Nature builds one for us every time a giant star dies. The core collapses under gravity, electrons merge with protons, and almost the whole thing turns to neutrons. What remains is, in a loose but honest sense, a single macroscopic atomic nucleus: a neutron star about 20 kilometers wide carrying the mass of a star.
One of the strangest members of that family turns up in our account of the twisting jet of the neutron star Circinus X-1, where the same kind of object does something no laboratory nucleus can, driving material outward in shocks that move at a tenth of the speed of light.
Table 1 — Size and density from the atom to a neutron star (standard nuclear-physics reference values, July 2026)
| Object | Typical diameter | Density |
|---|---|---|
| Atom (electron cloud) | ~10−10 m | mostly empty space |
| Atomic nucleus | ~10−15 m | ~1017 kg/m³ |
| Neutron star | ~20 km | a few × 1017 kg/m³ |
Look at the last column. A dead star and a helium nucleus sit in the same density neighborhood. Physics rarely repeats itself across 19 orders of magnitude in size, and when it does, the coincidence is worth stopping for.
- Up to 100,000 times smaller than its atom.
- More than 99.9 percent of the mass.
- A teaspoon would weigh 500 million metric tons, by our own arithmetic rather than by rounding up to a billion.
- Held together across a few femtometers by a force a hundred times stronger than electromagnetism, which is exactly why fusion needs a stellar core to happen at all.
Updated July 2026 with the teaspoon and grain-of-salt calculations worked out in full, and with a note on why the billion-ton figure quoted elsewhere does not follow from a density of 1017 kilograms per cubic meter.
Nineteen orders of magnitude, one density
A femtometer and twenty kilometers should have nothing to say to each other. They share a density because the same short-range force is doing the same job in both places, at scales separated by nineteen powers of ten. That is the sentence we would keep if we had to throw the rest of this article away.
Somewhere past the known elements, an island of stability may be waiting for the first laboratory bold enough to reach it. We would like to be writing about it when someone gets there.
FreeAstroScience publishes for readers who would rather see the arithmetic than the adjective. Check our numbers. A figure you can verify yourself is worth more than a figure you are asked to trust, and if ours are wrong we want to hear about it.
Gerd Dani, President of FreeAstroScience
Sources and further reading
This article draws on an editorial science dossier on atomic nuclei prepared for FreeAstroScience. The figures cited, a nuclear diameter near 10−15 meters, a density near 1017 kilograms per cubic meter, the magic numbers 2, 8, 20, 50 and 82, and the roughly 100-to-1 strength ratio between the strong nuclear force and electromagnetism, are standard reference values of modern nuclear physics. Both the teaspoon and the grain-of-salt calculations in the text are our own.
