The radius of a hydrogen atom is approximately 53 picometers (0.53 angstroms), based on the Bohr model’s ground-state calculation. That’s 5.3 × 10⁻¹¹ meters, roughly half a ten-billionth of a meter. But hydrogen doesn’t have a single, fixed radius. The number you use depends on whether you’re talking about a lone atom, a bonded atom, or the atom’s nucleus itself.
The Bohr Radius: Hydrogen’s Textbook Size
The most commonly cited value comes from the Bohr model of the atom, developed in 1913. In this model, the electron orbits the proton at specific allowed distances. The smallest orbit, called the ground state (where the electron sits at its lowest energy), has a radius of 53 picometers. This value is so fundamental to atomic physics that it has its own name: the Bohr radius, symbolized as a₀. It serves as a basic unit of length in quantum mechanics and appears throughout chemistry and physics calculations.
The Bohr model treats the electron like a planet orbiting a star, which isn’t quite how electrons actually behave. In reality, the electron exists as a probability cloud around the nucleus. There’s no sharp boundary where “the atom ends.” The 53 pm value represents the most probable distance between the electron and the proton, which is the point where you’re most likely to find the electron if you could take a snapshot.
Empirical vs. Calculated Radius
When scientists measure atomic radii experimentally, often through X-ray crystallography or diffraction techniques, they get a slightly different picture. The empirical atomic radius of hydrogen is about 25 picometers, roughly half the calculated Bohr value. This difference exists because experimental measurements typically capture hydrogen in bonded environments, where the electron cloud is pulled toward a neighboring atom and appears more compact. The calculated value of 53 pm represents the isolated, undisturbed atom.
Covalent Radius: Hydrogen in Molecules
When hydrogen forms a bond with another hydrogen atom (making H₂), the distance between the two nuclei is 74 picometers. Split that in half and you get hydrogen’s covalent radius: 37 pm. This is the measurement chemists use most often when predicting bond lengths in molecules. If you’re estimating how far apart atoms sit in a water molecule or an organic compound, the covalent radius is the relevant number.
Van der Waals Radius: The Outer Boundary
Atoms don’t just interact through bonds. Even unbonded atoms repel each other when they get too close, because their electron clouds start to overlap. The van der Waals radius defines how close two non-bonded atoms can comfortably sit. For hydrogen, this value has been surprisingly hard to pin down. Published estimates range from about 114 to 196 picometers depending on the method used.
A 2024 study in the Journal of Chemical Theory and Computation attempted to settle the question using multiple independent approaches. The researchers concluded that the van der Waals radius of a free hydrogen atom is 3.16 Bohr radii, which works out to roughly 167 picometers. This is the largest of hydrogen’s commonly cited radii, and it represents the effective “personal space” of a hydrogen atom in the context of weak intermolecular forces.
The Hydride Ion: When Hydrogen Gains an Electron
Hydrogen can also exist as a negatively charged ion (H⁻), called hydride, when it picks up a second electron. This extra electron dramatically inflates the atom. The hydride ion has a radius of about 134 picometers, making it roughly the same size as a fluoride or oxide ion. That’s more than twice the Bohr radius, because two electrons sharing the pull of a single proton spread out much farther than one electron would. The hydride ion is also highly polarizable, meaning its size can shift depending on what other atoms surround it.
The Proton: Hydrogen’s Nuclear Radius
At the other extreme, you can ask about the size of hydrogen’s nucleus, which is just a single proton. According to the 2022 CODATA recommended values from NIST, the proton’s root-mean-square charge radius is 0.84075 femtometers. A femtometer is a millionth of a billionth of a meter, making the proton about 63,000 times smaller than the atom it sits inside.
This number has its own fascinating backstory. For decades, experiments using electron-proton scattering and hydrogen spectroscopy measured the proton radius at roughly 0.88 femtometers. Then in 2010, a completely different technique replaced the electron in hydrogen with a muon (a heavier cousin of the electron) and found a radius of about 0.84 femtometers. The discrepancy, known as the proton radius puzzle, triggered a wave of new experiments. More recent precision measurements have converged toward the smaller value, but the disagreement with older methods isn’t fully resolved. The puzzle touches on some of the deepest questions in particle physics, including whether our best theory of how light interacts with matter needs revision.
Which Radius Should You Use?
The right number depends entirely on context:
- 53 pm (Bohr radius) for the size of an isolated hydrogen atom in its ground state
- 37 pm (covalent radius) for estimating bond lengths in molecules
- 25 pm (empirical radius) for the experimentally observed size in crystalline or bonded environments
- ~167 pm (van der Waals radius) for modeling how close non-bonded hydrogen atoms sit to neighbors
- 134 pm (hydride ion radius) for the negatively charged H⁻ species
- 0.84 fm (proton charge radius) for the size of the nucleus itself
If someone simply asks “what is the radius of hydrogen?” without further context, the answer they’re almost certainly looking for is 53 picometers. It’s the value taught in chemistry courses, listed on most periodic tables, and used as the starting point for understanding atomic structure.