Cubic Unit Cell Calculator

Crystal Lattice, Density, and Packing Factor Tool

Calculate key properties of cubic unit cells (simple, body-centered, face-centered) including density, atomic packing factor, atoms per cell, lattice parameter, and more. Enter your values and get instant results.

Examples

See how the calculator works with real elements.

Iron (Fe) - BCC

Body-Centered Cubic

Calculate for iron with BCC structure.

Edge Length (a): 286.65 pm

Atomic Radius (r): 124 pm

Molar Mass (M): 55.845 g/mol

Density: 7.87 g/cm³

Cubic Cell Type: Body-Centered Cubic (BCC)

Copper (Cu) - FCC

Face-Centered Cubic

Calculate for copper with FCC structure.

Edge Length (a): 361.49 pm

Atomic Radius (r): 128 pm

Molar Mass (M): 63.546 g/mol

Density: 8.96 g/cm³

Cubic Cell Type: Face-Centered Cubic (FCC)

Polonium (Po) - SC

Simple Cubic

Calculate for polonium with simple cubic structure.

Edge Length (a): 335 pm

Atomic Radius (r): 168 pm

Molar Mass (M): 209 g/mol

Density: 9.32 g/cm³

Cubic Cell Type: Simple Cubic (SC)

Aluminum (Al) - FCC

Face-Centered Cubic

Calculate for aluminum with FCC structure.

Edge Length (a): 404.95 pm

Atomic Radius (r): 143 pm

Molar Mass (M): 26.9815 g/mol

Density: 2.7 g/cm³

Cubic Cell Type: Face-Centered Cubic (FCC)

Other Titles
Understanding the Cubic Unit Cell Calculator: A Comprehensive Guide
Master cubic crystal structures, density, and atomic packing with this all-in-one tool.

What is a Cubic Unit Cell?

  • Definition and Types
  • Importance in Chemistry and Physics
  • Basic Parameters
A cubic unit cell is the simplest repeating unit in a cubic crystal lattice. There are three main types: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). Each type has a unique arrangement of atoms and different properties.
Types of Cubic Unit Cells

Common Cubic Unit Cell Examples

  • Iron (BCC)
  • Copper (FCC)

Step-by-Step Guide to Using the Calculator

  • Input Selection
  • Calculation Process
  • Interpreting Results
Select the cubic cell type, enter the edge length or atomic radius, and provide the molar mass. The calculator will compute all relevant properties, including density, APF, and atoms per cell.
How to Use the Calculator

Step-by-Step Examples

  • Aluminum (FCC) Example
  • Polonium (SC) Example

Real-World Applications of Cubic Unit Cells

  • Material Science
  • Crystallography
  • Industrial Uses
Cubic unit cells are fundamental in material science, crystallography, and various industries. They help determine material properties, design new materials, and analyze crystal structures.
Applications in Science and Industry

Practical Applications

  • X-ray Diffraction Analysis
  • Alloy Design

Common Misconceptions and Correct Methods

  • Misunderstanding Cell Types
  • Incorrect Unit Conversions
  • Overlooking APF
Many students confuse the different cubic cell types or make mistakes in unit conversions. This calculator ensures correct calculations and highlights the importance of APF and atom count.
Avoiding Common Errors

Misconceptions in Practice

  • Mixing up BCC and FCC
  • Forgetting to convert pm to cm

Mathematical Derivation and Examples

  • Formulas for Each Cell Type
  • Density Calculation
  • APF Calculation
The calculator uses standard formulas for cubic unit cells. For example, in BCC: a = 4r/√3, atoms per cell = 2, APF = 0.68. Density is calculated using the molar mass, Avogadro's number, and cell volume.
Key Formulas and Worked Examples

Mathematical Examples

  • Density of Iron (BCC)
  • APF of Copper (FCC)