Cell Volume Calculator

Inputs

Angles are in degrees. Lengths must be positive.

Crystal system *

Select the symmetry; the calculator applies the appropriate volume formula.

Length unit

Input lengths in this unit; output conversions are automatic.

Display volume as

This changes the headline volume display only.

a *

b *

c *

α (deg)

β (deg)

γ (deg)

Include measurement uncertainties (advanced)

Provide standard uncertainties σ for lengths (same unit as lengths) and angles (degrees). The tool estimates σV by finite differences.

σa

σb

σc

σα (deg)

σβ (deg)

σγ (deg)

Compute crystal density (optional)

Density uses ρ = Z·M /(N_A·V). Enter formula units per cell (Z) and molar mass M in g/mol.

Z (formula units)

M (g/mol)

Example Data Table

System	a	b	c	α	β	γ	Volume (Å³)
Cubic	5.431	5.431	5.431	90	90	90	160.16
Hexagonal	2.950	2.950	4.680	90	90	120	35.26
Monoclinic	7.120	8.990	10.120	90	104.2	90	625.6
Triclinic	6.200	7.400	8.100	88.0	92.0	75.0	356.9

Tip: Set length unit to Å and copy these values to test the calculator.

The most general unit-cell volume (triclinic) is computed from three edges and three angles:

V = a b c \sqrt{1 + 2\cos\alpha\cos\beta\cos\gamma - \cos^2\alpha - \cos^2\beta - \cos^2\gamma}

For common symmetry classes, this simplifies:

Angles are interpreted in degrees. Internally, the calculator converts to radians for trigonometric functions.