Cubic Cell Calculator
Use this cubic cell calculator to switch between atomic radius and lattice constant for simple cubic, body-centered cubic, and face-centered cubic structures.
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Run the calculator.
What This Cubic Cell Calculator Helps You Do
This page turns the standard cubic-cell geometry rules into a direct calculator so you can move between atomic radius and lattice constant without re-deriving the diagonal relationships each time. It also exposes the structural properties that usually matter alongside the geometry, such as atoms per cell and packing factor.
Because the output changes with simple cubic, BCC, and FCC selection, the page works both as a quick answer tool and as a compact crystal-structure reference.
How to Calculate Cubic Cell Calculator
- Choose the cubic cell type: Select simple cubic, BCC, or FCC because each structure uses a different geometry relation between radius and lattice constant.
- Choose the known value: You can solve from atomic radius or from lattice constant depending on the data you have.
- Read the derived crystal properties: The result includes the matching radius or lattice constant, atoms per cell, coordination number, packing factor, and cell volume.
- Keep units consistent: The calculator uses the same input and output unit for the geometry values so the interpretation stays direct.
Cubic Cell Calculator Formula
| Variable | Meaning | Unit |
|---|---|---|
| a | Lattice constant of the cubic cell | angstroms or nm |
| r | Atomic radius | angstroms or nm |
| APF | Atomic packing factor | dimensionless |
| Z | Atoms per unit cell | count |
Use the worked examples below to check how the formula behaves with real values. If the result looks unexpected, verify the unit assumptions and the meaning of each variable before interpreting the answer.
Worked Examples
- Cell type: FCC
- Atomic radius: 0.143 nm
Result: Lattice constant is 0.4045 nm.
FCC cells pack efficiently and produce a larger lattice constant than the atomic diameter because atoms touch along the face diagonal.
- Cell type: Simple cubic
- Atomic radius: 1.67 A
Result: Lattice constant is 3.34 A.
In a simple cubic cell, atoms touch directly along the edge, so the lattice constant is just twice the radius.
- Cell type: BCC
- Lattice constant: 2.86 A
Result: Atomic radius is about 1.239 A.
For BCC cells, contact occurs along the body diagonal, which changes the geometry relation.
- Cell type: FCC
- Atomic radius: 0.125 nm
Result: APF is 0.740 and atoms per cell is 4.
FCC is the most closely packed cubic structure and reaches the highest cubic packing factor.
How to Interpret Your Results
| Range | Meaning | Action |
|---|---|---|
| Simple cubic | Lowest packing efficiency of the three cubic structures. | Expect APF about 0.524 and only one atom per unit cell. |
| Body-centered cubic | Intermediate packing with body-diagonal contact. | Use the BCC geometry relation instead of the edge-contact relation. |
| Face-centered cubic | Most efficient cubic packing. | Expect APF about 0.740 and four atoms per unit cell. |
Frequently Asked Questions
References
Last reviewed: March 2026