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 in a given volume. For precious metals, density is of particular practical importance: it enables quick, non-destructive authenticity checks and is indispensable when calculating melt values.

Definition and formula

Density is 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 used almost exclusively (1 g/cm³ = 1,000 kg/m³). Water at 4 °C has, by definition, a density of exactly 1.000 g/cm³ and serves as the reference for specific gravity — a dimensionless ratio that numerically matches density in g/cm³.

Densities of the main precious metals compared

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

Density of alloys

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

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

The exact density of an alloy can be approximated from the volume fractions of the constituents (rule of mixtures), but deviates slightly from this due to lattice distortions. This shows that the fineness of an alloy directly influences the density — a relationship that authenticity testing exploits.

Density as an authenticity feature

Density is hard to fake because it is a fundamental material constant. The most dangerous known counterfeit, however, exploits precisely a near-match in density: tungsten counterfeits consist of a tungsten core (19.25 g/cm³) coated with a thin layer of gold. The overall density then lies so close to that of pure gold (19.32 g/cm³) that simple weighing tests fail.

Precise density-based authenticity methods:

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

The coin weight checker and the authenticity check on this site use target-density values to detect deviations for known coins.

A practical formula: calculating volume from mass

Anyone wanting to determine the melt value of scrap gold or broken gold needs the fine weight. If the volume of a piece is known (e.g. through 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 — helpful 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, the volume grows and the density falls. For gold the linear expansion coefficient is approx. 14.2 × 10⁻⁶ K⁻¹. At room temperature (20 °C) the tabulated values apply; at gold's melting point (1,064 °C) the density of the melt is about 17.4 g/cm³. For everyday authenticity testing this deviation is negligible, provided measurements are taken at room temperature.

Density in industry and numismatics

In coin production, density tolerances are tightly defined. The Krugerrand (916 gold, 22 carat) has a fixed mass of 33.93 g and a diameter of 32.77 mm — values based on the target density of the 91.67% gold alloy. Deviations from the target weight of more than 0.1% are treated as a warning sign.

In industry, density plays a role in planning storage capacity: one kilogram of gold takes up about 51.8 cm³, considerably 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. At 19.32 g/cm³, gold is almost impossible to imitate even among candidate counterfeit materials — only tungsten comes dangerously close. Anyone wishing to test coins or bars ideally combines the density test with the magnet test and a visual inspection of the hallmarks.