Calculate theoretical crystal density from unit-cell data or two-phase composite density from mass or volume fraction, with unit conversions and measured-density comparison.

A cubic cell has equal edges a and 90° angles. Match the count Z and molar mass to the same chemical formula.

A positive effective count may include partial occupancy. Match its chemical basis to molar mass.

Measured density comparison

Blank omits comparison; zero is an entered zero density.

Theoretical Density Formula

For the crystal model, theoretical density is calculated as follows:

ρ = (n × A) / (V × NA)
  • Where ρ is the density (g/cm^3)
  • n is the number of atoms per unit cell (for elemental crystals). For compounds, use Z = number of formula units per unit cell.
  • A is the atomic weight / molar mass (g/mol) of the element (for compounds, use the molar mass of the formula unit).
  • V is the unit-cell volume (cm^3/cell). If your volume is in Å^3, convert using 1 Å^3 = 10^-24 cm^3.
  • NA is Avogadro’s constant (6.02214076×10^23 mol^-1).

To calculate crystal density, multiply the matching atom or formula-unit count by its molar mass, then divide by unit-cell volume in cm³ and Avogadro’s constant. This calculator takes lattice lengths in Å or nm, not a direct volume input. It computes a³ for a cubic cell, or abc√(1 + 2 cosα cosβ cosγ − cos²α − cos²β − cos²γ) for a general cell, then converts 1 ų = 10⁻²⁴ cm³.

Theoretical Density Definition

Theoretical crystal density is calculated from the cell geometry, composition and matching molar mass for an ideal fully dense structure at the specified lattice parameters. The separate two-phase composite models assume additive constituent volumes with no voids or reaction volume change: volume fractions give ρ = f₁ρ₁ + (1−f₁)ρ₂, while mass fractions give ρ = 1/(w₁/ρ₁ + (1−w₁)/ρ₂). Do not substitute one fraction basis for the other.

What is the theoretical maximum density?

The theoretical density of a crystalline material can be calculated using ρ = (n*A)/(V*NA) (or ρ = (Z*M)/(V*NA) for compounds). It is an ideal model for the stated structure and conditions, not a universal material maximum. A measured value may be lower or higher when composition, temperature, defects or measurement basis differ. Relative density is measured/theoretical × 100%; the signed density deficit is 100% minus that ratio. A negative deficit is not negative porosity, and a density difference alone does not establish porosity.

How to calculate a theoretical density?

  1. For a crystal, first determine the matching atom or formula-unit count per cell. A positive fractional effective count may represent partial occupancy, but its composition basis must match the molar mass.
  2. Next, use the atomic molar mass for an elemental atom or the formula molar mass for the stated compound. For an alloy or partially occupied structure, use a consistent composition model for both the count and molar mass.
  3. Next, enter the cubic edge a, or all three lengths and angles for a general cell. The calculator derives the cell volume from those lattice parameters. General-cell angles must each be between 0° and 180°, satisfy every strict triangle inequality, and total less than 360°.
  4. Finally, select Calculate to find the theoretical density. For a composite instead, choose the correct mass- or volume-fraction model, enter both constituent densities and the phase 1 percentage, and use the remaining percentage for phase 2. An optional measured density may be left blank to omit comparison; an entered zero is compared as zero.