Use this cubic cell calculator to find edge length, atomic radius, volume, density, and structure facts for SC, BCC, and FCC crystals.
Advanced options
How to use our Cubic Cell Calculator
- Choose Cubic structure as simple cubic (SC), body-centered cubic (BCC), or face-centered cubic (FCC), then choose Find values from to match the one main value you already know.
- Enter the active input: Atomic radius (A), Edge length (A), or both Density (g/cm^3) and Molar mass (g/mol). If needed, open Advanced options and change Length unit for radius and edge to A, nm, or pm.
- Click Calculate to see Edge length, Atomic radius, Unit cell volume, Atoms per unit cell, Touching neighbors, Packing factor, and the Structure rule used.
- Sanity-check the result: Atoms per unit cell should be 1 for SC, 2 for BCC, or 4 for FCC, and Packing factor should stay near 0.5236, 0.6802, or 0.7405 for those same structures.
- If Density does not appear, check Note. In radius or edge mode, density only shows when Molar mass (g/mol) is also filled in.
Definitions
Cubic structure: The atom pattern inside the cube. This calculator uses simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) [1].
Atomic radius: The size of one atom in the hard-sphere model used for crystal geometry.
Edge length: The length of one side of the cubic unit cell. It is also called the lattice parameter or cell constant.
Unit cell volume: The space inside one repeating cube, found from edge length cubed.
Density: Mass per volume, shown here in g/cm^3.
Molar mass: The mass of 1 mole of atoms or formula units, shown in g/mol.
Atoms per unit cell: The effective number of atoms that belong to one cubic cell: 1 for SC, 2 for BCC, and 4 for FCC.
Touching neighbors: The number of nearest atoms around one atom in the ideal structure. This is the coordination number.
Packing factor: The fraction of the unit-cell volume filled by atoms in the ideal hard-sphere picture.
Structure rule used: The geometry equation that connects atomic radius and edge length for the chosen cubic structure.
Common mistakes and quick fixes
Mistake: Entering Atomic radius (A) while Find values from is set to edge length or density mode.
Fix: Switch Find values from to Atomic radius, or enter the matching active field instead.
Mistake: Typing Edge length (A) in pm or nm without changing Length unit for radius and edge .
Fix: Set the unit selector first so Edge length and Atomic radius are interpreted and shown in the same unit.
Mistake: Leaving Molar mass (g/mol) blank and expecting a Density result in radius or edge mode.
Fix: Add Molar mass (g/mol) if you want Density , or read the Note and use the geometry results only.
Mistake: Using 0 or a negative number for Density (g/cm^3) , Atomic radius (A) , or Edge length (A) .
Fix: Enter a value greater than 0 in the active input because unit-cell size and density must be positive here.
Mistake: Mixing up structure names and then thinking the Structure rule used is wrong.
Fix: Recheck Cubic structure . SC uses a = 2r, BCC uses a = 4r/sqrt(3), and FCC uses a = 2*sqrt(2)*r.
Mistake: Reading Touching neighbors as atoms per cube.
Fix: Use Atoms per unit cell for how many atoms belong to one cell, and Touching neighbors for nearest neighbors around each atom.
Limitations & Key Assumptions / Boundary Conditions
- The calculator assumes an ideal cubic crystal with perfectly hard, touching spheres. Real materials can differ because bonding and measured atomic size are not perfectly rigid.
- Only three structures are supported: SC, BCC, and FCC. It does not cover hexagonal close-packed, diamond cubic, or non-cubic cells.
- Density is only computed when both unit-cell size and Molar mass (g/mol) are available.
- In density mode, the result depends directly on the entered Density (g/cm^3) and Molar mass (g/mol). Wrong units will give wrong geometry.
- Packing factor and Touching neighbors are fixed ideal values for the selected structure and do not change with temperature, defects, or impurities.
- Very small or very large inputs may round in the display, even though the internal math still uses the entered value.
Methodology
Core relationships
The calculator first reads the chosen cubic structure and assigns the fixed structure values: atoms per cell, touching neighbors, and packing factor.
n = 1 for SC; n = 2 for BCC; n = 4 for FCC
a = 2r for SC; a = 4r/sqrt(3) for BCC; a = 2*sqrt(2)*r for FCC
r = a/2 for SC; r = sqrt(3)*a/4 for BCC; r = a/(2*sqrt(2)) for FCC
V_cell = a^3
rho = (n*M)/(N_A*V_cell)
a = ((n*M)/(N_A*rho))^(1/3)
APF = n*(4/3)*pi*r^3/a^3
How each solve choice works
If you solve from Atomic radius, the calculator uses the structure rule to find edge length, then cubes the edge length to get Unit cell volume. If Molar mass (g/mol) is also filled in, it then computes Density.
If you solve from Edge length, it reverses the matching structure rule to find Atomic radius, then finds volume and optional density.
If you solve from Density and molar mass, it rearranges the density equation to find edge length first, then finds atomic radius from the chosen structure.
Unit conversions
Density uses g/cm^3, so edge length must be converted to centimeters before volume is used in the density formula. The calculator uses 1 A = 1e-8 cm, 1 nm = 1e-7 cm, and 1 pm = 1e-10 cm. The Avogadro constant is 6.02214076 x 10^23 per mole.
Mini example
Suppose you choose FCC and enter an atomic radius of 1.43 A.
a = 2*sqrt(2)*r = 2*sqrt(2)*1.43 = 4.0447 A
V_cell = a^3 = (4.044650788e-8 cm)^3 approx 6.6167e-23 cm^3
If you also enter a molar mass of 63.546 g/mol, the calculator uses n = 4 for FCC and finds density near 6.379 g/cm^3.
rho = (4*63.546)/(6.02214076e23*6.6167e-23) approx 6.379 g/cm^3
Assumptions behind the outputs
The structure-specific geometry for SC, BCC, and FCC follows the standard cubic unit-cell model [3]. Packing factor and touching-neighbor values are ideal geometric values, so measured real-world samples can differ because of defects, temperature, or composition changes.