Unit Cell Volume Calculator
Calculate the volume of a crystallographic unit cell for all seven crystal systems based on lattice parameters and angles.
Calculation Parameters
Specify your stoichiometry inputs.
Calculated Result
Expert Tip
One Ångström (Å) is 10⁻¹⁰ meters, meaning 1 ų equals exactly 10⁻²⁴ cubic centimeters (cm³).
How this Calculator Works
This calculator determines crystallographic unit cell volume using lattice side dimensions and angles. Select the crystal geometry system and adjust variables:
- Crystal System: Determines the geometric rules and which axes/angles are independent.
- Side a, b, c: Unit cell edge lengths in Ångströms (Å).
- Angles α, β, γ: Inner unit cell angles in degrees (°).
The results are computed instantly and updated in the results panel on the right.
Formula & Methodology
Where:
- V: Unit cell volume (ų).
- a, b, c: Lattice parameters (edge lengths).
- α, β, γ: Lattice angles.
Step-by-Step Calculation Example
To calculate the volume of a monoclinic unit cell manually, follow these steps:
- Identify the input parameters. For example:
- Crystal System = Monoclinic
- a = 5.0 Å, b = 5.0 Å, c = 6.0 Å
- Beta Angle (β) = 95°
- Apply the formula:
1. Convert angle to radians: β = 95 * (π / 180) ≈ 1.658 rad 2. Apply formula: V = a * b * c * sin(β) 3. Calculate V = 5.0 * 5.0 * 6.0 * sin(95°) = 150.0 * 0.9962 ≈ 149.43 ų
- Verify the calculated value which is updated instantly in the results panel on the right.
Frequently Asked Questions
What is the unit cell volume formula for a cubic system? ▼
V = a³, where a is the cubic edge length.
What is the unit cell volume formula for a hexagonal system? ▼
V = a² × c × sin(60°) = 0.866 × a² × c.
Why is unit cell volume important in materials science? ▼
Unit cell volume combined with formula unit count (Z) allows precise determination of theoretical crystal density.