Density of Magnesium HCP Metal Calculator

Calculator Inputs

Calculation mode

Material name

Chemical symbol

Molar mass

g/mol

Primary density unit

Decimal places

Lattice Parameters

Lattice parameter a

a unit

a uncertainty

Use the selected a unit.

Lattice parameter c

c unit

c uncertainty

Use the selected c unit.

Atomic Radius Method

Atomic radius

Radius unit

Radius uncertainty

c/a ratio

c/a ratio uncertainty

HCP Cell Convention

Unit-cell representation

Atoms per selected cell

Sample Mass and Volume

Sample mass

Mass unit

Mass uncertainty

Sample volume

Volume unit

Volume uncertainty

Porosity Correction

Theoretical density

Theoretical density unit

Porosity

Porosity uncertainty

Temperature Adjustment

Reference temperature

°C

Calculation temperature

°C

Expansion coefficient along a

µm/m·K

Expansion coefficient along c

µm/m·K

Reference and Display Options

Reference density

Reference density unit

Use scientific notation

Formula Used

Magnesium normally forms a hexagonal close-packed crystal structure. Density equals unit-cell mass divided by unit-cell volume. Correct cell conventions prevent sixfold errors during density calculations.

Crystallographic cell: V = (√3 / 2)a²c

Full HCP prism: V = (3√3 / 2)a²c

Cell mass: m = nM / N_A

Theoretical density: ρ = m / V

Measured density: ρ = sample mass / sample volume

Porosity correction: ρ_bulk = ρ_theoretical(1 − P/100)

Thermal expansion: L_T = L₀[1 + α(T − T₀)]

How to Use This Calculator

Select a calculation mode and enter known measurements. Choose matching units before submitting the form. Review all warnings before using results for engineering decisions.

Choose lattice, radius, specimen, porosity, or temperature mode.
Enter values with their matching units and uncertainties.
Select the correct HCP cell convention when required.
Choose output precision and the preferred density unit.
Calculate, compare, copy, print, or export the results.

Worked Magnesium Example

Use the magnesium preset for standard starting values. Replace defaults with laboratory or published measurements. Compare theoretical density with measured density to identify porosity.

Input	Example value	Purpose
Lattice parameter a	3.2094 Å	Basal-plane dimension
Lattice parameter c	5.2108 Å	Hexagonal-axis dimension
Molar mass	24.305 g/mol	Mass per mole of magnesium atoms
Cell convention	Crystallographic	Uses two atoms and its matching volume
Reference density	1.738 g/cm³	Comparison benchmark

Theoretical and Bulk Density

Theoretical density assumes a perfect and fully dense crystal. Bulk density includes pores, defects, and manufacturing variations. Their difference helps estimate internal voids and material quality.

Common Assumptions

Results depend on accurate dimensions and consistent unit choices. Thermal expansion is modeled as linear over temperature. Real alloys may require composition-specific data and correction factors.

The selected cell volume matches its atom count.
The material is chemically uniform and predominantly HCP.
Linear expansion coefficients remain suitable across the temperature interval.
Uncertainty terms are independent and sufficiently small.

Density Unit Conversion Table

Starting value	Equivalent value
1 g/cm³	1000 kg/m³
1 g/cm³	0.0361273 lb/in³
1 g/cm³	62.428 lb/ft³
1 kg/m³	0.001 g/cm³
1 kg/m³	0.001 mg/mm³

Frequently Asked Questions

What does HCP mean?

HCP means hexagonal close-packed. It describes a repeating atomic arrangement. Magnesium commonly adopts this crystal structure near room temperature.

Why are two cell conventions available?

Crystallography often uses a smaller primitive-equivalent hexagonal cell. Textbooks may show a larger full prism. Each volume must use its matching atom count.

Why can atom counts cause large errors?

Density depends directly on mass per selected cell. A mismatched count changes cell mass incorrectly. The calculator warns about common HCP convention mismatches.

What is the ideal HCP c/a ratio?

The geometric ideal is approximately 1.633. Real metals can differ from this value. Magnesium is close but not exactly ideal.

How does porosity change density?

Porosity reduces solid material within the bulk volume. Greater porosity lowers measured bulk density. The correction assumes pores contain negligible solid mass.

Can this calculator handle magnesium alloys?

Yes, by replacing molar mass and structural data. Alloy density may require composition-weighted properties. Phase mixtures can make a single HCP model insufficient.

How is temperature applied?

The calculator expands a and c independently. It uses linear expansion over the entered interval. Large temperature ranges may need nonlinear material data.

How is uncertainty estimated?

Independent relative uncertainties are combined by root-sum-square propagation. The formula changes with the selected mode. Correlated errors require a more detailed analysis.

Why might my result differ from a handbook?

Handbook values depend on temperature, purity, and measurement method. Lattice constants also vary between sources. Use data matching your exact sample conditions.

Disclaimer

This calculator provides educational and preliminary engineering estimates. Verify critical values using traceable laboratory or handbook data. Temperature, purity, alloying, and defects can change actual density.