Cubic Unit Cell Calculator — SC, BCC, FCC
Select a cubic crystal structure (SC, BCC or FCC), enter the lattice parameter in picometres, and instantly find the atomic radius, atoms per unit cell, packing efficiency, coordination number and cell volume.
Crystal structure
pm
Radius of one atom calculated from the lattice parameter
Unit Cell
4 atoms- 1
Radius factor (Face-Centred Cubic (FCC))
√2 ÷ 4 = 0.353553Atoms touch along the face diagonal (length a√2) — r = a√2/4. - 2
Atomic radius (pm)
400 × 0.353553 = 141.42
How does this calculator work?
For a cubic unit cell, the atomic radius depends on structure: SC: r = a/2; BCC: r = a√3/4; FCC: r = a√2/4. Packing efficiencies are SC 52.4 %, BCC 68.0 %, FCC 74.0 %. Atoms per cell: SC = 1, BCC = 2, FCC = 4. Enter the lattice parameter to get all values instantly.
Formula
How this is calculated
In solid-state chemistry and physics, a unit cell is the smallest repeating building block of a crystal lattice. For cubic systems, the unit cell is a cube of side length a (the lattice parameter). Three common cubic arrangements differ in where atoms sit:
Simple Cubic (SC) places one atom at each of the eight corners, each shared between eight adjacent cells, giving 8 × 1/8 = 1 atom per cell. Atoms touch along the cell edge, so the atomic radius r = a/2. SC is the most open structure with only ≈ 52.4 % packing efficiency (the fraction of space occupied by hard spheres).
Body-Centred Cubic (BCC) adds one atom at the cell centre on top of the eight corner atoms, giving 2 atoms per cell. Atoms touch along the body diagonal (length a√3), so r = a√3/4. Packing efficiency is ≈ 68.0 %. Many metals (iron, tungsten, chromium) adopt BCC.
Face-Centred Cubic (FCC / CCP) places atoms at all corners plus one at the centre of each face (6 faces × 1/2 = 3, plus 1 = 4 atoms per cell). Atoms touch along the face diagonal (length a√2), giving r = a√2/4. FCC achieves the highest cubic packing efficiency of ≈ 74.05 % and is adopted by many dense metals (copper, aluminium, gold, silver). Packing efficiencies are exact analytical values derived from the sphere-touching condition and are independent of the actual element.
Frequently asked questions
A BCC unit cell contains 2 atoms: 8 corner atoms each shared among 8 cells (8 × 1/8 = 1) plus 1 atom fully enclosed at the centre, giving 1 + 1 = 2.
FCC atoms touch along face diagonals, allowing spheres to pack more tightly (≈ 74.0 %) than BCC (≈ 68.0 %) where atoms touch only along the body diagonal. FCC (and HCP) are the densest possible packings of equal spheres.
The coordination number is the count of nearest-neighbour atoms touching each atom: SC = 6, BCC = 8, FCC = 12. A higher coordination number generally means stronger metallic bonding and a denser, harder material.
Also known as
TG we-Calculate Editorial Team. (2026). Cubic Unit Cell Calculator — SC, BCC, FCC [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cubic-cell-calculator
TG we-Calculate Editorial Team. "Cubic Unit Cell Calculator — SC, BCC, FCC." TG we-Calculate. 2026. https://we-calculate.com/calculator/cubic-cell-calculator.
TG we-Calculate Editorial Team, "Cubic Unit Cell Calculator — SC, BCC, FCC," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cubic-cell-calculator
@misc{wecalculate_cubic_cell_calculator, title = {Cubic Unit Cell Calculator — SC, BCC, FCC}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cubic-cell-calculator}}, year = {2026}, note = {TG we-Calculate} }
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