Density

Density (symbol: ρ, Greek rho) is one of the most fundamental material properties in physics and chemistry. It describes how much mass is contained within a given volume. For precious metals, density is of particular practical importance: it enables rapid, non-destructive authenticity testing and is indispensable for calculating melt values.

Definition and Formula

Density is derived from the quotient of mass and volume:

ρ = m / V

ρ  = Density [g/cm³ or kg/m³]
m  = Mass [g or kg]
V  = Volume [cm³ or m³]

In the SI system, the base unit is kg/m³. In metallurgical practice, g/cm³ is almost exclusively used (1 g/cm³ = 1,000 kg/m³). Water at 4 °C has a density of exactly 1.000 g/cm³ by definition and serves as the reference for specific gravity — a dimensionless ratio that is numerically identical to density in g/cm³.

Densities of the Most Important Precious Metals Compared

Gold and platinum thus rank among the densest naturally occurring elements. This property is deeply rooted in physics: both metals possess a face-centred cubic (FCC) crystal structure with an exceptionally efficient atomic packing density, combined with a high atomic weight.

Density of Alloys

Pure fine gold (999.9 ‰) has a density of 19.32 g/cm³. Once gold is alloyed, the density changes noticeably depending on the alloying partner:

• 750 gold (18 karat): approx. 15.5–17.8 g/cm³ (depending on silver/copper content)
• 585 gold (14 karat): approx. 13.0–14.9 g/cm³
• 333 gold (8 karat): approx. 10.5–12.0 g/cm³

The precise density of an alloy can be approximately calculated from the volume fractions of its constituents (mixing rule), but deviates slightly due to lattice distortions. This shows: the fineness of an alloy directly influences its density — a relationship that authenticity testing exploits.

Density as an Authenticity Feature

Density is difficult to fake because it is a fundamental material constant. The most dangerous known forgery, however, exploits a density similarity: tungsten forgeries consist of a tungsten core (19.25 g/cm³) coated with a thin layer of gold. The overall density is so close to that of pure gold (19.32 g/cm³) that simple weighing fails.

Precise methods for density-based authenticity testing:

1. Archimedes' principle (hydrostatic weighing): The object is weighed in air and then submerged in water. The difference in weight gives the volume, from which density is derived. Very accurate, but requires a precision scale with undertray hook.
2. Pycnometer: Laboratory method with a defined liquid volume — very precise.
3. Sigma Metalytics / eddy current testing: Measures the electrical resistance of the metal, which indirectly correlates with density.
4. X-ray fluorescence analysis (XRF): Determines composition non-destructively — not a direct density measurement, but complementary.

The coin weight checker and authenticity check on this site use reference density values to detect deviations in known coins.

Practical Formula: Calculating Volume from Mass

Anyone wishing to determine the melt value of scrap or broken gold needs the fine weight. If the volume of a piece is known (e.g. via water displacement), the mass can be calculated:

m = ρ × V

Example: Gold bar, 10 cm³ volume (fine gold 999)
m = 19.32 g/cm³ × 10 cm³ = 193.2 g

Conversely, the volume can be derived from the measured weight — useful when the shape is irregular. For the melt value calculator, entering the weight and fineness is then sufficient.

Temperature Dependence

Density is not an absolute constant. As temperature rises, metal expands, volume increases, and density decreases. For gold, the linear expansion coefficient is approximately 14.2 × 10⁻⁶ K⁻¹. At room temperature (20 °C), the tabulated values apply; at the melting point of gold (1,064 °C), the density of the melt is approximately 17.4 g/cm³. For everyday authenticity testing, this deviation is negligible as long as measurements are taken at room temperature.

Density in Industry and Numismatics

In coin minting, density tolerances are tightly defined. The Krugerrand (916 gold, 22 karat) has a specified mass of 33.93 g with a diameter of 32.77 mm — values based on the reference density of the 91.67% gold alloy. Deviations from the target weight of more than 0.1% are considered an indicator for testing.

In industry, density plays a role in planning storage capacities: one kilogram of gold occupies only about 51.8 cm³, significantly less space than one kilogram of silver (approx. 95.3 cm³).

In Brief

Density is the most reliable and oldest physical method for assessing the authenticity of precious metals. Gold at 19.32 g/cm³ is almost impossible to imitate among counterfeit candidates — only tungsten comes dangerously close. Anyone wishing to test coins or bars ideally combines density testing with the magnet test and a visual inspection of hallmarks.