How Is Atomic Radius Measured? Covalent, Metallic and van der Waals Radii

Ask for the radius of a chlorine atom and you might be told 99 pm, 102 pm, 175 pm or 181 pm, depending on which book you open. None of these numbers is wrong. They are answers to slightly different questions, and understanding why they differ is one of the best ways to understand what an atom really is.

The problem: atoms have no edge

A marble has a surface. You can put a ruler against it and read off a diameter. An atom does not work like that. Its electrons are described by orbitals, and the probability of finding an electron fades away gradually as you move out from the nucleus. It never drops suddenly to zero. There is no skin to measure.

So any “radius” of an atom has to be a definition: we choose some measurable distance and agree to call half of it (or part of it) the radius. The three main choices depend on how the atom is sitting when we measure it:

• bonded to an identical atom by a covalent bond → covalent radius
• packed with identical atoms in a metal → metallic radius
• merely touching a neighbouring atom without bonding → van der Waals radius

A fourth, the ionic radius, applies when the atom has gained or lost electrons. Each is measured differently, and each gives a different number for the same element.

What we actually measure: distances between nuclei

Nobody measures a radius directly. What experiments measure very precisely is the distance between the centres of two atoms, that is, between their nuclei. The main tools are:

• X-ray diffraction of crystals, which reveals how atoms are arranged in a solid and the spacing between them;
• electron diffraction of gases, useful for small molecules;
• microwave (rotational) spectroscopy, which gives very accurate bond lengths for gas-phase molecules from how fast they rotate.

These methods give internuclear distances to a precision of about a picometre or better. The radius is then carved out of that distance by a rule.

Covalent radius: half a bond

The simplest case is a molecule made of two identical atoms joined by a single covalent bond. In a chlorine molecule, Cl₂, the two nuclei sit 199 pm apart. Chemists define the covalent radius of chlorine as half of that: about 99–100 pm.

The same idea works for hydrogen. The H–H bond length in H₂ is 74 pm, so the covalent radius of hydrogen is about 37 pm. For carbon, the C–C single bond in diamond is 154 pm, giving a covalent radius of about 77 pm.

The useful thing about covalent radii is that they are roughly additive. If you want to estimate a C–Cl bond length, you add the covalent radius of carbon to that of chlorine: 77 + 99 ≈ 176 pm. The measured value in chloromethane is about 178 pm, which is close. This additivity is why covalent radii are so handy in structural chemistry.

A few complications are worth knowing:

• Bond order matters. A C=C double bond (134 pm) and a C≡C triple bond (120 pm) are shorter than a C–C single bond, so tables usually quote single-bond covalent radii and list separate values for multiple bonds.
• Different tables disagree slightly. Modern compilations average thousands of crystal structures and may give chlorine as 102 pm rather than 99 pm. Small differences like this come from the averaging method, not from mistakes.
• Polar bonds shrink a little. When the two atoms have very different electronegativities, the bond is often shorter than the simple sum predicts.

Metallic radius: half the distance between neighbours in a metal

Metals are not made of separate molecules, so there is no “bond” in the usual sense. Instead, X-ray diffraction gives the dimensions of the crystal’s repeating unit, the unit cell. From those dimensions you can work out the distance between nearest-neighbour atoms, and half of that is the metallic radius.

Take sodium. It crystallises in a body-centred cubic structure with a cell edge of about 429 pm. In that structure, nearest neighbours lie along the body diagonal, at a distance of (√3 ⁄ 2) × 429 ≈ 372 pm. Half of that gives a metallic radius of about 186 pm.

Copper has a face-centred cubic structure with an edge of about 361.5 pm. Nearest neighbours lie along a face diagonal, at 361.5 ⁄ √2 ≈ 256 pm, so the metallic radius of copper is about 128 pm.

Metallic radius depends a little on how many neighbours each atom has, so tables usually correct all values to the same coordination number (12) to make them comparable.

Van der Waals radius: the “personal space” of an atom

Now imagine two atoms that are not bonded, such as two argon atoms in solid argon, or two chlorine atoms belonging to different Cl₂ molecules in a crystal. They come close enough to touch but no closer, because their electron clouds repel. Half the closest distance between such non-bonded atoms is the van der Waals radius.

Van der Waals radii are always larger than covalent radii, often by 70 pm or more, because a bond pulls two atoms into each other’s electron clouds while a mere contact does not. For chlorine, the covalent radius is about 99 pm, but the van der Waals radius is about 175 pm. The periodic table on this site uses van der Waals radii for its atomic radius heatmap, because they describe the size of an atom that isn’t sharing electrons with anything. Some values from the same dataset:

Element	Van der Waals radius (pm)
Hydrogen	120
Carbon	170
Oxygen	152
Chlorine	175
Argon	188
Potassium	275
Caesium	343

Van der Waals radii are the least precise of the family, because “touching” is a fuzzy idea and the contact distance changes with the environment. They are still very useful: they define the space-filling models you see in molecular graphics, and they explain why some molecules cannot twist into certain shapes.

Ionic radius: splitting a distance between two different ions

In an ionic crystal such as sodium chloride, X-ray diffraction gives the distance between a Na⁺ nucleus and the nearest Cl⁻ nucleus (about 282 pm). But how much of that belongs to each ion? There is no unique answer. Chemists have to fix the radius of one reference ion (historically oxide or fluoride) and then work out the others by subtraction across many crystals. Different reference choices give slightly different tables, which is why you should always use ionic radii from one consistent source. Our guide to ionic radius covers how cations shrink and anions swell compared with their atoms.

Why the same element has several radii

Put the ideas together for chlorine:

Kind of radius	What is measured	Approximate value
Covalent	Half the Cl–Cl bond in Cl₂	99–102 pm
Van der Waals	Half the contact distance between separate molecules	175 pm
Ionic (Cl⁻)	Share of the Na–Cl distance in salts	181 pm

The spread is not a failure of measurement. It reflects real physics: a bonded atom overlaps its neighbour, a non-bonded atom keeps its distance, and an extra electron makes the cloud swell.

Calculated radii

There is one more family: radii calculated from quantum mechanics rather than measured. One common approach takes the distance from the nucleus to the point of maximum electron density in the outermost orbital. These values are handy because they exist for every element, including ones that are hard to study experimentally, and they follow periodic trends very smoothly. They are usually smaller than the measured covalent radii and shouldn’t be mixed with them in calculations.

How the trends look whichever radius you use

The good news is that the big patterns survive every definition:

• Across a period, radius decreases. Each step adds a proton and an electron to the same shell. The rising effective nuclear charge pulls the shell in.
• Down a group, radius increases. Each step adds a whole new shell further from the nucleus.

So caesium is always among the largest atoms and fluorine or helium among the smallest, whichever table you trust. The atomic radius trend article goes deeper into the reasons and the exceptions, such as the lanthanide contraction.

Common mistakes

• Mixing radius types in one calculation. Adding a covalent radius to a van der Waals radius gives a meaningless distance.
• Treating tabulated radii as exact. They are averages over many compounds and can shift by several picometres from one structure to another.
• Comparing an atom’s radius with an ion’s radius from a different table. Use a single source when comparing sizes.
• Thinking the atom stops at its radius. Electron density continues beyond any quoted radius; the number marks a useful boundary, not a wall.

Key takeaways

• Atoms have no sharp edge, so a radius is always defined through a measured distance between nuclei.
• Covalent radius is half the bond length between identical bonded atoms; values are roughly additive for estimating bond lengths.
• Metallic radius is half the nearest-neighbour distance in a metal crystal.
• Van der Waals radius is half the closest contact between non-bonded atoms and is always the largest of the three.
• Ionic radius needs an agreed reference ion, so use one consistent table.
• Whatever the definition, radius shrinks across a period and grows down a group. You can see it on the interactive periodic table.