Density Measurement (Archimedes)
Also: Archimedean density measurement, hydrostatic weighing, underwater weighing
A non-destructive method for the authenticity testing of precious metals by measuring the specific density according to the Archimedean principle.
Density measurement according to the Archimedean principle is one of the most reliable and at the same time most accessible methods for testing precious-metal pieces for authenticity. Every material has a characteristic specific density — a fixed ratio of mass to volume — which changes measurably through alloys, counterfeit materials or cavities. The method is non-destructive, requires no chemicals and is reproducible with simple means.
The Archimedean principle
The Greek mathematician Archimedes of Syracuse (c. 287–212 BC) recognised that a body immersed in liquid experiences a buoyant force exactly equal to the weight of the displaced liquid. For the density measurement of precious metals this means:
ρ_object = (m_air / (m_air − m_water)) × ρ_water
Legend:
ρ_object= the density of the test object sought (g/cm³)m_air= weight of the object in air (g)m_water= weight of the object when immersed in water (g)ρ_water= density of water (≈ 0.9982 g/cm³ at 20 °C)
The difference m_air − m_water corresponds to the buoyancy and thus to the volume of the displaced water. Dividing the air weight by this volume gives the density of the object.
Step-by-step instructions
- Weigh the object dry — use a precision balance with at least 0.01 g resolution; note the value as
m_air. - Prepare the water — distilled or filtered water at as constant a temperature as possible (20 °C is ideal). Read off the water temperature and density ρ_water from a table, or assume ≈ 0.9982 g/cm³.
- Set up the underwater rig — suspend the object on a fine thread or wire below the pan into the water without touching the bottom of the container. Many precision balances offer a hook for suspension.
- Weigh underwater — note the value as
m_water. - Calculate the density — apply the formula; compare the result with the reference values in the table.
Reference densities of key precious metals and counterfeit materials
| Material | Density (g/cm³) | Note |
|---|---|---|
| Gold 999.9 (fine gold) | 19.32 | Reference value |
| Gold 750 (18 carat) | 15.1–16.4 | depending on alloy |
| Gold 585 (14 carat) | 13.0–14.5 | depending on alloy |
| Tungsten | 19.25 | most common gold counterfeit |
| Platinum 999 | 21.45 | significantly heavier than gold |
| Silver 999 | 10.49 | Reference value |
| Silver 835 | 10.0–10.2 | typical for cutlery |
| Lead | 11.34 | older counterfeits |
| Brass | 8.4–8.7 | cheap counterfeits |
| Copper | 8.96 | hard to detect when gold-plated |
The table shows why tungsten is the most dangerous counterfeit method: at 19.25 g/cm³ it lies so close to the fine-gold value of 19.32 g/cm³ that only high-precision measurements (±0.01 g/cm³) or supplementary methods — such as X-ray fluorescence analysis or ultrasonic testing — allow a reliable distinction.
Strengths and limits
Strengths:
- Non-destructive and free of chemicals
- Reliably detects cavities, fillings and false alloys
- Low cost: a precision balance with a suspension hook and a vessel of water are enough
- Equally suitable for bars, coins and jewellery
Limits and sources of error:
- Air bubbles on the object distort the buoyancy (degrease the object before measuring)
- Very small objects (under 1 g) require microbalances for reliable results
- A tungsten core in gold-clad bars can bring the overall density close to the reference value if the ratio is right — here an additional ultrasonic test or drill sample is indicated
- Alloys of unknown composition only give a suspicion value, not an unambiguous fineness
- Uneven surfaces (embossing, reeding) and adhering air require careful preparation
Combination with other testing methods
For a reliable assessment, density measurement is recommended as the first stage in a multi-stage testing protocol:
- Density measurement — quick rough classification (counterfeit or plausible)
- Magnet test — rules out ferromagnetic counterfeit materials
- Ping test — gives clues about cavities
- X-ray fluorescence analysis (XRF) — exact element composition at the surface
- Acid test — chemical proof when gold-plated counterfeits are suspected
For coins and bars to be valued against the current gold price, density measurement offers a solid first orientation before a dealer or refinery formally assesses the piece.
Practical tip: temperature correction
Water has its greatest density at 4 °C (1.0000 g/cm³). At a room temperature of 20 °C it is 0.9982 g/cm³. Anyone wanting to measure to ±0.05 g/cm³ should measure the actual water temperature and use the corresponding density value from a reference table. For most home tests the approximate value of 0.998 g/cm³ is sufficient.
In brief
Archimedean density measurement is a simple, reliable and inexpensive tool for the first authenticity check of precious metals. It detects most counterfeits immediately — only high-quality tungsten counterfeits require supplementary methods. Combined with weight and dimension checks via the Coin Weight Checker, it covers the broad spectrum of everyday testing situations.