Density Test (Archimedes)
Also: Archimedean density measurement, hydrostatic weighing, underwater weighing
A non-destructive way to check whether a piece of precious metal is genuine by measuring its specific density using Archimedes' principle of buoyancy.
Measuring density using Archimedes' principle is among the most dependable and accessible techniques for confirming that a bullion piece is what it claims to be. Every substance has its own specific density — a fixed ratio of mass to volume — and that value shifts in a measurable way whenever a counterfeit alloy, a hidden filler or an internal cavity is present. The method destroys nothing, needs no chemicals and can be repeated with modest equipment.
The principle behind it
The Greek mathematician Archimedes of Syracuse (roughly 287–212 BC) observed that a body immersed in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. Applied to precious metals, this gives us:
ρ_object = (m_air / (m_air − m_water)) × ρ_water
Key:
ρ_object= the density we want to find (g/cm³)m_air= weight of the item in air (g)m_water= weight of the item while submerged (g)ρ_water= density of water (≈ 0.9982 g/cm³ at 20 °C)
The difference m_air − m_water represents the buoyant force and therefore the volume of displaced water. Dividing the dry weight by that volume yields the density of the object.
Step by step
- Weigh the item dry — use a precision balance resolving to at least 0.01 g and record the reading as
m_air. - Prepare the water — distilled or filtered water at as steady a temperature as possible (20 °C is ideal). Read the density ρ_water from a table or simply assume ≈ 0.9982 g/cm³.
- Rig the submerged setup — suspend the item on a thin thread or wire below the pan so it hangs freely in the water without touching the base of the container. Many precision scales include a hook for below-balance weighing.
- Weigh it submerged — record the reading as
m_water. - Calculate the density — apply the formula and compare against the reference table.
Reference densities of key metals and common fakes
| Material | Density (g/cm³) | Note |
|---|---|---|
| Gold 999.9 (fine gold) | 19.32 | reference value |
| Gold 750 (18 carat) | 15.1–16.4 | depends on the alloy |
| Gold 585 (14 carat) | 13.0–14.5 | depends on the alloy |
| Tungsten | 19.25 | the most common gold fake |
| Platinum 999 | 21.45 | noticeably heavier than gold |
| Silver 999 | 10.49 | reference value |
| Silver 835 | 10.0–10.2 | typical for cutlery |
| Lead | 11.34 | older forgeries |
| Brass | 8.4–8.7 | cheap fakes |
| Copper | 8.96 | hard to spot when gold-plated |
The table explains why tungsten is the most dangerous forgery material: at 19.25 g/cm³ it sits so close to fine gold's 19.32 g/cm³ that only high-precision measurements (±0.01 g/cm³) or supporting methods — such as X-ray fluorescence analysis or ultrasound testing — can tell them apart reliably.
Strengths and limits
Strengths:
- Non-destructive and chemical-free
- Reliably exposes cavities, fillers and incorrect alloys
- Low cost: a precision balance with a suspension hook and a vessel of water suffice
- Works equally well on bars, coins and jewellery
Limits and sources of error:
- Air bubbles clinging to the item distort the buoyancy (degrease it before measuring)
- Very small items (under 1 g) need a microbalance for trustworthy figures
- A tungsten core inside a gold-clad bar can push the overall density close to the reference value if the proportions are right — here an additional ultrasound test or drill sample is warranted
- Alloys of unknown composition yield only a suspicion, not a definitive fineness
- Uneven surfaces (reliefs, reeding) and trapped air call for careful preparation
Combining it with other tests
For a sound verdict, use the density test as the first stage of a layered checking routine:
- Density test — quick coarse triage (fake or plausible)
- Magnet test — rules out ferromagnetic fake materials
- Ping test — hints at hidden cavities
- X-ray fluorescence analysis (XRF) — precise surface element composition
- Acid test — chemical confirmation where gold-plated fakes are suspected
For coins and bars you intend to value against the current gold price, the density test gives a solid first orientation before a dealer or refinery appraises the piece formally.
Practical tip: temperature correction
Water reaches its maximum density at 4 °C (1.0000 g/cm³). At a room temperature of 20 °C it drops to 0.9982 g/cm³. If you want accuracy to within ±0.05 g/cm³, measure the actual water temperature and use the matching density value from a reference table. For most home checks the approximation of 0.998 g/cm³ is perfectly adequate.
In brief
The Archimedean density test is a simple, reliable and inexpensive tool for a first authenticity check on precious metals. It catches most fakes immediately — only high-quality tungsten forgeries call for supporting methods. Combined with weight and dimension checks via the Coin Weight Checker, it covers the broad range of everyday verification situations.