What this calculator does
Cubic unit cell (packing efficiency) works out edge length, atoms per cell and packing efficiency for SC, BCC and FCC lattices. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaSimple cubic: a = 2r, 1 atom/cell, efficiency π/6. BCC: a = 4r/√3, 2 atoms/cell, efficiency π√3/8. FCC: a = 4r/√2, 4 atoms/cell, efficiency π/(3√2)
The inputs explained
| Field | What to enter |
|---|---|
| Lattice type | Choose from Simple cubic, Body-centred cubic, Face-centred cubic. |
| Atomic radius (pm) | A number, measured in pm. Starts at 128. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with atomic radius
Every other input is held at the calculator’s starting values while atomic radius varies. Select any row to load that scenario into the calculator.