Atomic Radius Calculator

The atomic radius is a measure of the size of an atom — specifically the distance from the nucleus to the outermost electron shell. Because electrons do not have a sharply defined boundary, atomic radius is always defined operationally: it depends on how the measurement is made and in what chemical environment. This atomic radius calculator lets you look up three standard definitions for any of the most commonly studied elements, and converts the result into four unit systems in one step.

Atomic radii are measured in picometers (pm), where 1 pm = 10⁻¹² m. They are also frequently expressed in angstroms (Å), where 1 Å = 100 pm = 10⁻¹⁰ m, and in nanometers (nm), where 1 nm = 1000 pm. Even the largest atoms have radii below 300 pm, underscoring just how incredibly small atomic dimensions are.

Atomic size is not merely an abstract property — it governs bond lengths, molecular geometry, packing in crystal lattices, ionization energy, electronegativity, and reactivity. Chemists use atomic radius data daily when predicting whether a substitution reaction is geometrically feasible, determining whether a foreign atom will fit into a crystal lattice, or rationalizing why one element is more reactive than another. Understanding periodic trends in atomic radius is therefore one of the most fundamental skills in general and physical chemistry.

The three types of atomic radius recognized in this calculator — empirical, covalent, and van der Waals — arise from different experimental methods and reflect different aspects of an atom's effective size. Each has distinct uses and is appropriate for different chemical contexts. Choosing the correct radius type is essential for accurate bond-length estimation and correct interpretation of molecular models.

This calculator provides three operationally defined radii for each element. Understanding how each is measured helps you choose the right one for your application.

Empirical (Crystal) Radius

The empirical radius (sometimes called the metallic or crystal radius) is derived from X-ray diffraction measurements of crystalline solids. For metals, it is calculated as half the internuclear distance between two adjacent identical atoms in the crystal lattice. For non-metals that do not typically form metallic crystals, empirical radii are estimated from average interatomic distances observed across multiple crystal structures. These values are listed in standard reference tables and are the ones displayed by default in this atomic radius calculator. Empirical radii reflect how tightly atoms pack in the condensed phase and are widely used in materials science.

Covalent Radius

The covalent radius is defined as half the internuclear distance between two identical atoms joined by a single covalent bond. For example, the Cl–Cl bond length in Cl₂ is 198 pm, so the covalent radius of chlorine is 99 pm. When two different atoms form a bond, their individual covalent radii can be added to estimate the bond length — a useful predictive tool. Covalent radii are the most directly relevant for molecular geometry and bond-length calculations. This calculator uses single-bond (sigma) covalent radii throughout.

Van der Waals Radius

The van der Waals radius represents the effective size of a non-bonded atom — specifically half the distance between two atoms of the same element that are in contact through non-covalent van der Waals forces (but not chemically bonded). These radii are derived from crystal packing data for noble gases and from the closest non-bonded contact distances in molecular crystals. Van der Waals radii are always larger than covalent radii for the same element because the electron cloud extends further when not compressed by a shared bond. They are essential for space-filling molecular models, docking calculations in drug design, and understanding molecular recognition.

One of the most important patterns in the periodic table is the trend in atomic radius, and this atomic radius calculator makes it easy to compare values and confirm these patterns for yourself. Two overarching trends govern atomic size: variation across a period (left to right) and variation down a group (top to bottom).

Trend Across a Period (Left to Right)

As you move from left to right across any period of the periodic table, atomic radius generally decreases. The reason is that each successive element adds one more proton to the nucleus and one more electron to the same valence shell. The additional proton increases the nuclear charge (Z), pulling all electrons more strongly toward the nucleus. Because the new electron enters the same principal energy level (n), it provides very little additional shielding of the nuclear charge for the other electrons. The net effect is a higher effective nuclear charge (Z_eff) experienced by each electron, which contracts the electron cloud. For example, in Period 3, the empirical radius decreases from sodium (Na, 190 pm) to chlorine (Cl, 79 pm) — a reduction of more than 58% across just seven elements.

Trend Down a Group

Moving down a group (column) in the periodic table, atomic radius generally increases. Each new period adds a new principal quantum shell further from the nucleus, which automatically increases the size of the atom. Additionally, inner-shell electrons shield the valence electrons from the full nuclear charge, partially counteracting the increase in proton count. The result is that valence electrons feel a relatively constant Z_eff but reside in progressively higher energy shells at greater average distances from the nucleus. Potassium (K, 243 pm) is far larger than sodium (Na, 190 pm), which in turn is much larger than lithium (Li, 167 pm) — all members of Group 1.

The Role of d-Block Contraction

The trend is not perfectly monotonic. In the transition metal series, the d electrons are added to inner orbitals and provide poor shielding, causing the d-block contraction: atomic radii do not increase as steeply, and in some cases decrease slightly, across the 3d, 4d, and 5d series. This explains why Cu (145 pm) and Zn (142 pm) are smaller than expected if a simple left-to-right contraction were continuing across the full period.

This atomic radius calculator automatically converts every selected radius into four units: picometers (pm), angstroms (Å), nanometers (nm), and meters (m). Understanding these conversions prevents unit errors when using atomic radius data in bond-length calculations, crystallography, or molecular modeling software.

Picometers (pm) are the standard unit in modern chemistry for reporting atomic and ionic radii. The SI prefix "pico" means 10⁻¹², so 1 pm = 10⁻¹² m. All IUPAC tables and most textbooks published after 1980 use picometers. The calculator stores all radii internally in picometers and uses this as the reference for all conversions.

Angstroms (Å), though not an SI unit, remain widespread in crystallography, spectroscopy, and molecular modeling — particularly in older literature and in software such as VESTA, CrystalMaker, and many molecular dynamics packages. The conversion is exact: 1 Å = 100 pm, so dividing picometers by 100 gives angstroms. The calculator applies: r(Å) = r(pm) / 100.

Nanometers (nm) are common in nanotechnology and biophysics. Since 1 nm = 1000 pm, the conversion is: r(nm) = r(pm) / 1000. For example, the van der Waals radius of carbon (170 pm) converts to 0.170 nm, a value frequently cited in discussions of graphene layer spacing and nanotube geometry.

Meters (m) are used when atomic radius values must be incorporated into SI calculations, such as in expressions for atomic volume, electromagnetic cross-sections, or quantum mechanical wavelength comparisons. The conversion is: r(m) = r(pm) × 10⁻¹².

The calculator also computes the estimated atomic volume by treating the atom as a perfect sphere using the formula V = (4/3) × π × r³. While atoms are not hard spheres, this approximation provides a useful order-of-magnitude estimate of the space occupied by an atom, and is the standard approach in discussions of atomic packing efficiency in crystal structures. The volume is reported in both cubic angstroms (ų) — the most common unit in crystallography — and implicitly in cubic picometers. Note that the van der Waals radius gives the largest estimated volume, as it represents the outermost boundary of the atom's effective size.

For any given element, the three radius values follow a consistent ordering: covalent radius < empirical radius < van der Waals radius in almost all cases. This ordering reflects the physical reality of how electron clouds behave in different environments.

The covalent radius is smallest because forming a bond compresses the electron clouds of both atoms toward the internuclear axis. The shared electron pair occupies the region between the nuclei, and the mutual attraction pulls both nuclei closer together than they would otherwise be. The result is that the covalent radius is typically 5–20% smaller than the empirical radius for the same element.

The empirical radius falls in the middle. In a metallic crystal or a packed solid, atoms touch each other but no directional bond is formed. The electron cloud extends freely to the point where repulsion from neighboring atoms begins. This gives an intermediate size — larger than the covalent radius but smaller than the free-atom van der Waals size.

The van der Waals radius is largest because it measures the outer boundary of the atom when only weak London dispersion forces hold the neighbors apart. No bonding compression occurs, and the full extent of the electron cloud is sampled. For hydrogen, the van der Waals radius (120 pm) is nearly four times larger than the covalent radius (31 pm) — a dramatic difference that has major consequences for the steric interactions of hydrogen in molecular structures.

A practical consequence of this ordering: when building a molecular model in software that uses van der Waals radii, atoms appear to overlap significantly when bonds are present. This "overlap" is not unphysical — it simply reflects that the bonding distance is much shorter than the sum of van der Waals radii, which is the expected outcome for atoms that share electrons. This is precisely why space-filling models (CPK models) use van der Waals radii but still show atoms touching or slightly overlapping along bond axes.

Use this atomic radius calculator to look up and compare all three radius types for elements across the periodic table, and to convert any selected radius instantly into the unit system required by your application — whether you are calculating bond lengths, estimating lattice parameters, or preparing a molecular visualization.

Atomic radius data underpins a surprisingly broad range of practical calculations and design decisions across chemistry, physics, and engineering. The following applications illustrate why having accurate, instantly accessible atomic radius values — as provided by this atomic radius calculator — matters in real scientific work.

Predicting bond lengths: The most direct application is estimating the length of a covalent bond between two different elements. The Schomaker–Stevenson rule (and more recent improvements by Pyykkö and Atsumi) add the covalent radii of the two atoms and apply a small electronegativity correction to predict bond length. For a C–N bond, for example, the sum of the covalent radii is 76 + 71 = 147 pm, which agrees closely with the experimentally observed C–N single bond length of about 147 pm.

Crystal structure design and solid solutions: In materials science and solid-state chemistry, atoms can substitute for one another in a crystal lattice only if their sizes are similar. The Hume-Rothery rules state that extensive solid solubility requires the solute and solvent atoms to differ in radius by less than about 15%. Comparing empirical radii with this atomic radius calculator instantly tells whether a given substitution is geometrically feasible.

Ion size and ionic compounds: When atoms gain electrons to form anions, they become larger (increased electron–electron repulsion, same nuclear charge); when they lose electrons to form cations, they contract significantly (fewer electrons, same nuclear charge). Comparing the neutral-atom empirical radius with tabulated ionic radii reveals the magnitude of these effects — for example, Na has an empirical radius of 190 pm but the Na⁺ ion has a radius of only about 102 pm.

Molecular accessibility and drug design: Van der Waals radii define the steric envelope of each atom and are the foundation of computational drug docking. When a drug molecule enters an enzyme active site, the van der Waals radii of both the drug and the residue atoms determine whether they can approach each other without energetically costly overlap. Programs like AutoDock and Schrödinger Glide use exactly these radii internally.

Effective nuclear charge and shielding: Combining atomic radius trends with the Slater screening constants provides a quantitative picture of how inner electrons shield the valence electrons. Elements with higher effective nuclear charge have smaller radii — a relationship that can be explored systematically using this calculator to compare elements across periods and groups.