Crystal System Identifier
Enter a unit cell’s three edge lengths and three angles and see which of the seven crystal systems it belongs to, using the standard symmetry rules.
Crystal system
How the classification works
Each crystal system is defined by constraints on the cell’s edges (a, b, c) and angles (alpha, beta, gamma). Cubic requires all three edges equal and all three angles at 90°. Tetragonal relaxes that to two equal edges and a distinct third, still with right angles throughout. Orthorhombic keeps all three angles at 90° but allows every edge to differ. Hexagonal sets two edges equal with a 120° angle between them and 90° elsewhere. Trigonal, in its rhombohedral setting, has three equal edges and three equal angles that are not 90°. Monoclinic allows unequal edges with two right angles and one tilted angle, and triclinic — the least symmetric — has no equal edges and no angle fixed at all.
The tool checks these constraints from most restrictive to least, with a small tolerance for rounding, so a cell close to but not exactly at a boundary still classifies sensibly.
Frequently Asked Questions
What are the seven crystal systems?
Every crystalline mineral's atomic lattice belongs to one of seven systems — cubic (isometric), tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic — defined by the relationships between the unit cell's three edge lengths (a, b, c) and three interaxial angles (alpha, beta, gamma). Cubic is the most symmetric, with all three edges equal and every angle a right angle; triclinic is the least, with no edges equal and no angle fixed at 90°.
Where do 'edge lengths' and 'angles' actually come from?
They describe the smallest repeating box of a mineral's crystal lattice, normally measured by X-ray diffraction in a lab. This tool is for exploring the classification rules with known or textbook values — it doesn't measure a physical specimen for you.
How is this different from crystal habit?
Crystal system is about the internal lattice symmetry; crystal habit is the external shape a specimen actually grew into (needles, plates, cubes, clusters) which is affected by growth conditions and can look different even within one system. Two specimens can share a crystal system and look nothing alike, or share a habit while belonging to different systems.
Why does the tool describe trigonal minerals as 'rhombohedral'?
Trigonal minerals are classified here by their rhombohedral cell (three equal edges, three equal angles not equal to 90°). Many trigonal minerals, including quartz and calcite, are also commonly described using an alternative hexagonal-shaped cell for convenience — if you enter that hexagonal-setting cell instead, this simplified tool will report it as Hexagonal.
Educational tool only, not a substitute for X-ray diffraction or a laboratory determination of crystal structure.