Chemistry
Cubic Cell Calculator
Link atomic radius, lattice parameter and density for simple, body-centred and face-centred cubic crystals.
Your inputs
Change any value to update the result instantly.
Lattice parameter a
404.465 pm
Atoms per unit cell Z
4
Theoretical density
2.7084 g/cm³
Unit cell volume
66.1673 nm³ × 10⁻³
Packing efficiency
74.05 %
Geometry used
Atoms touch along the face diagonal
Packing efficiency comes out near 52% for simple cubic, 68% for body-centred and 74% for face-centred, which is the closest packing of equal spheres.
What this calculator does
Links atomic radius, lattice parameter, packing efficiency and theoretical density for cubic unit cells.
What your result means
The edge length of the unit cell and the density that geometry implies.
Formula and working
ρ = Z·M / (N_A·a³); SC a = 2r, BCC a = 4r/√3, FCC a = 2√2·r
- 1
Collect the inputs
Cubic lattice type = 3; Atomic radius r = 143 pm; Molar mass M = 26.98 g/mol
- 2
Apply the formula
ρ = Z·M / (N_A·a³); SC a = 2r, BCC a = 4r/√3, FCC a = 2√2·r
- 3
Result
Lattice parameter a = 404.465 pm
Frequently asked questions
Symbols and assumptions
- a
- Lattice parameter
- Z
- Atoms per unit cell
- r
- Atomic radius
- N_A
- Avogadro constant
- • Hard-sphere atoms touching along the stated direction.
- • Z is 1, 2 or 4 for simple, body-centred and face-centred cubic.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • Real crystals have defects and thermal expansion, so measured density is slightly lower.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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