Unit Cell Density Calculator
Crystal density from lattice type and edge length.
Work out Unit Cell Density. Crystal density from lattice type and edge length. Free, with no account and nothing to download.
Picometres, as crystallographic data is usually published. Copper is 361.5 pm.
Crystal density
8.9351 g/cm³
4 atoms per cell — face-centred cubic
ρ = ZM / (N_A·a³). Z is atoms per unit cell and it follows from the lattice, not the element: 1 for simple cubic, 2 for body-centred, 4 for face-centred. Getting Z wrong changes the answer by a whole factor, and it is the most common mistake here. Density falls with the cube of the edge length, so a small error in a lattice parameter is amplified threefold. Run in reverse this is how Avogadro's number was pinned down before 2019: measure a crystal's density and its lattice spacing by X-ray diffraction, and N_A drops out. Since the SI redefinition the constant is exact and the calculation runs the other way.
How the Unit Cell Density Calculator works
Pick the lattice type, enter the molar mass and the unit cell edge in picometres, and this returns the density. Atoms per cell follows from the lattice — 1 simple cubic, 2 body-centred, 4 face-centred — and getting it wrong changes the answer by a whole factor.
Also known as: crystal density calculator · fcc density calculator · atoms per unit cell calculator · lattice parameter to density
Frequently asked questions
How do I calculate density from a unit cell?
ρ = ZM / (N_A·a³), where Z is atoms per cell, M is molar mass, N_A is Avogadro's number and a is the edge length in centimetres.
How many atoms are in a unit cell?
Simple cubic has 1, body-centred cubic 2, and face-centred cubic 4. The counts come from sharing: a corner atom is split between eight cells, a face atom between two, and a body-centre atom belongs entirely to one.
Why picometres?
Because that is the unit crystallographic data is published in. Copper's edge is 361.5 pm. The calculation converts to centimetres internally so the density comes out in g/cm³.
Can this be used to find Avogadro's number?
It used to be one of the best ways — measure a crystal's bulk density and its lattice spacing by X-ray diffraction, and N_A drops out. Since the 2019 SI redefinition the constant is exact, so the calculation now runs only in this direction.
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