Math / CALCULATOR

Equal-Sphere Crystal Packing Fraction

Equal-Sphere Crystal Packing Fraction with a worked example and explicitly bounded inputs.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

Enter lattice.

Formula

SC=π/6; BCC=√3 π/8; FCC=π/(3√2).
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • Ideal identical touching spheres in one of three specified crystal lattices; not arbitrary container or random packing.

Example Calculation

Example inputs
  • Lattice: Simple cubic

Lattice = sc. Primary result: 0.5235987755982988.

Frequently asked questions

How do I use this calculator?

Enter lattice. The result updates automatically. Use Reset to restore the example values.

What method does it use?

SC=π/6; BCC=√3 π/8; FCC=π/(3√2).. Ideal identical touching spheres in one of three specified crystal lattices; not arbitrary container or random packing.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.