Cubic Cell Calculator

In crystallography, a cubic unit cell is the repeating building block of a crystal lattice — and its geometry determines a material's density, atomic packing, and bonding behavior. Select your Cubic Cell Type (SC, BCC, or FCC) and Calculation Type, then enter your Atomic Radius, Edge Length, or Atomic Mass to get the Primary Result alongside secondary outputs: Coordination Number, Packing Efficiency, and Atoms per Unit Cell.

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Results

Primary Result

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Coordination Number

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Packing Efficiency

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Atoms per Unit Cell

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Frequently Asked Questions

Which are the three types of cubic cells?

The three types of cubic cells are Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). SC has atoms only at the corners, BCC has an additional atom at the center, and FCC has atoms at the corners and face centers.

What are the lattice parameters of a cubic cell?

In a cubic cell, all three lattice parameters (a, b, c) are equal, and all angles are 90°. The lattice parameter 'a' represents the edge length of the cubic unit cell.

How do I calculate the lattice constant of a cubic cell?

The lattice constant depends on the cubic structure: For SC: a = 2r, for BCC: a = 4r/√3, and for FCC: a = 2√2r, where 'a' is the lattice constant and 'r' is the atomic radius.

Why are there different formulas for different cubic structures?

Different cubic structures have different arrangements of atoms. The formulas account for how atoms touch along different directions - edge, body diagonal, or face diagonal - depending on the crystal structure.

How accurate are these calculations for real materials?

These calculations are based on ideal hard sphere models and provide good approximations for many materials. Real crystals may have slight deviations due to factors like thermal vibrations and electronic interactions.

Can this calculator be used for ionic crystals?

This calculator is designed for metallic crystals with single atom types. For ionic crystals with different sized cations and anions, specialized calculations considering both ion sizes are needed.

What is the coordination number for each cubic structure?

The coordination number (number of nearest neighbors) varies by structure: Simple Cubic has 6, Body-Centered Cubic has 8, and Face-Centered Cubic has 12 nearest neighbors.

How do I determine the packing efficiency?

Packing efficiency is the fraction of space occupied by atoms. It's 52.4% for SC, 68.0% for BCC, and 74.0% for FCC structures, calculated from the volume of atoms divided by unit cell volume.