theoretical density
If you know exactly what is inside one repeating box and how big the box is, you can weigh the box and divide by its volume to get the material's density — no laboratory scale required. That calculated value is the theoretical density.
The formula is rho = (n times A) divided by (V_C times N_A), where n is the number of atoms per unit cell, A is the atomic weight in grams per mole, V_C is the unit-cell volume, and N_A is Avogadro's number, 6.022 x 10^23 per mole. For copper (FCC): n = 4, A = 63.55, and a = 0.3615 nm, which gives rho of about 8.9 g/cm^3 — right in line with what a scale measures.
This links the atomic scale to a bulk property you can actually weigh, and it is the honest pore-free density. Real parts almost always measure a little lower, because vacancies, porosity, and grain-boundary volume take up space. The ratio of measured to theoretical density is a standard gauge of how fully dense a cast or sintered part really is.
Copper (FCC): n = 4, A = 63.55 g/mol, a = 0.3615 nm so V_C = a^3 = 4.72 x 10^-23 cm^3. Then rho = (4 times 63.55) / (4.72 x 10^-23 times 6.022 x 10^23) which is about 8.9 g/cm^3 — right on the measured value.
From one unit cell to a bulk density you can check on a scale.
Measured density is usually a touch below theoretical because of vacancies, porosity, and grain-boundary volume; a large gap flags voids or an incorrectly assumed structure.