Ionic Radius from Unit Cell Calculator

Find ionic or atomic radius directly from lattice parameter with rigorous formulas and clear steps. Choose structure type set ratio or known radius and see distances in angstroms and picometers. Educational mode explains geometry validation checks ensure physically consistent outputs. Supports SC BCC FCC NaCl CsCl ZnS and Fluorite with formulas displayed for clarity.

Inputs
Results

Enter inputs and press Calculate to see results and worked steps.

Reference formulas
SC r = a/2
BCC r = (√3/4) a
FCC r = (√2/4) a
NaCl r⁺ + r⁻ = a/2
CsCl r⁺ + r⁻ = (√3/2) a
ZnS r⁺ + r⁻ = (√3/4) a
Fluorite r⁺ + r⁻ = (√3/4) a
FAQs

How do I choose the correct structure?

Select SC, BCC, or FCC for elemental solids that pack as identical spheres. Choose NaCl, CsCl, ZnS, or Fluorite for binary ionic solids with those archetypal motifs.

Which units should I use for the lattice parameter?

Enter a in Å or nm. The calculator converts nm to Å internally, and reports outputs in Å and pm.

Can I compute individual ionic radii instead of just the sum?

Yes. Provide the radius ratio k = r⁺/r⁻ to split the sum, or specify either r⁺ or r⁻ directly to obtain the counterpart by difference.

What assumptions does this model make?

Ions are treated as hard spheres touching along the nearest-neighbor line. Real crystals deviate due to covalency, polarization, coordination changes, and temperature.

Why do my results look unphysical?

If a known radius exceeds the neighbor distance d, the other radius becomes negative. This indicates inconsistent inputs or a structure assignment that does not match the material.

How should I pick the rounding?

Three decimals are typical for crystallography summaries. Increase decimals for sensitivity checks, decrease for presentation. Rounding is applied to displayed values only, not internal calculations.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.