Ionic Radius Calculator

Ionic radius is the effective radius of an ion in a crystal lattice, representing the distance from the nucleus to the outermost electrons when the ion is surrounded by neighboring ions. Unlike atomic radius, which describes neutral atoms, ionic radius accounts for the change in electron cloud size that occurs when atoms gain or lose electrons. This parameter is essential for predicting crystal structures, bond lengths, and the physical properties of ionic compounds.

When an atom loses electrons to form a cation, the remaining electrons are held more tightly by the nucleus because the effective nuclear charge increases. This causes cations to be significantly smaller than their parent atoms. For example, sodium metal has an atomic radius of 190 pm, but the Na⁺ ion has a radius of only 102 pm — a 46% reduction. Conversely, when an atom gains electrons to form an anion, increased electron-electron repulsion expands the electron cloud, making anions larger than their neutral atoms. The chloride ion (181 pm) is more than twice the size of a chlorine atom (79 pm).

The most widely used ionic radii are the Shannon radii, published by R.D. Shannon in 1976. These values are derived from a systematic analysis of over 1000 crystal structures and provide radii for each ion at specific coordination numbers. The standard reference values are for coordination number 6 (octahedral geometry), but radii for other coordination numbers are also available. Always compare ionic radii at the same coordination number for meaningful comparisons.

This calculator provides ionic radius data for common cations and anions, converts between picometers, angstroms, and nanometers, and compares ionic radii with the corresponding neutral atom radii to show the size change upon ionization.

The size change when forming an ion from a neutral atom can be quantified as a percentage change.

Follow these steps to look up ionic radius data and compare with atomic radii:

1. Select an Ion: Choose from the dropdown list, which is organized into two groups: cations (positive ions) and anions (negative ions). Each entry shows the ion symbol, element name, and ionic radius in picometers.
2. View the Radius: The calculator displays the ionic radius in three units: picometers (pm), angstroms (A), and nanometers (nm). The standard Shannon ionic radius for coordination number 6 is shown.
3. Compare with Neutral Atom: The results show the radius of the corresponding neutral atom and calculate the percentage size change. Cations shrink (negative percentage) while anions expand (positive percentage). A visual comparison shows the relative sizes of the neutral atom and ion.

The ionic radius trends are displayed: cations are smaller than parent atoms (fewer electrons, same nuclear charge), anions are larger (more electrons, increased repulsion), and in isoelectronic series, more protons means smaller radius.

The calculator provides several types of information about each ion:

Ionic Radius: The Shannon ionic radius for the selected ion at coordination number 6. This is the standard value used for crystal structure predictions and bond length calculations. The radius is given in picometers (1 pm = 10⁻¹² m), angstroms (1 A = 100 pm), and nanometers (1 nm = 1000 pm).

Ion Type: Whether the ion is a cation (positive, formed by losing electrons) or anion (negative, formed by gaining electrons). Cations are always blue-coded and anions are red-coded for easy identification.

Neutral Atom Comparison: The radius of the corresponding neutral atom is shown alongside the ionic radius. The visual comparison helps you see the magnitude of the size change. Cations are always smaller than their parent atoms, while anions are always larger.

Size Change: The absolute change in picometers and the percentage change. For example, Na⁺ is 88 pm smaller than Na (a 46.3% decrease), while Cl⁻ is 102 pm larger than Cl (a 129% increase). These changes reflect the fundamental physics of electron removal and addition.

Trends: The calculator highlights key periodic trends: ionic radius decreases across a period for isoelectronic ions, increases down a group, and cations are always smaller than anions of the same element.

Ionic radius data is essential in crystallography for solving crystal structures and predicting new materials. When crystallographers determine an unknown structure, they use ionic radii to calculate expected bond lengths and validate their models. Materials scientists use ionic radii to design new ceramics, superconductors, and battery materials by matching ion sizes to specific crystal lattice sites.

Geochemistry relies on ionic radii to understand mineral formation and elemental distribution in rocks. Trace elements substitute for major elements in minerals based on similar ionic radii and charges — a process called ionic substitution. For example, Mg²⁺ and Fe²⁺ have similar radii (72 pm vs 78 pm), allowing them to substitute freely in olivine minerals in Earth's mantle.

Biological systems exploit ionic radius differences for ion selectivity. Potassium channels in cell membranes are designed to pass K⁺ (138 pm) while rejecting Na⁺ (102 pm), even though Na⁺ is chemically similar. The selectivity filter of these channels has precisely sized carbonyl oxygen atoms that coordinate K⁺ perfectly but cannot effectively stabilize the smaller Na⁺ ion.

Water purification technology uses ion exchange resins that selectively capture ions based on their size and charge. Water softeners replace Ca²⁺ and Mg²⁺ with Na⁺, while deionization systems remove all dissolved ions. Understanding ionic radii helps engineers design more efficient ion exchange materials.