Pt 31.857 Pd 29.967 Rh 144.678 Au 74.586 Ag 0.947

How to Accurately Calculate the Density of Bullion Bars and Coins


How to Accurately Calculate the Density of Bullion Bars and Coins

Blog #2 ,Ami Gur , May 29-2024

תמונה ללינקדאין עמי
תמונה ללינקדאין עמי

Calculating the density of bullion is a crucial process in confirming the authenticity and quality of precious metal products. The density of an object is defined as its mass divided by its volume. While measuring the weight of a bullion piece is straightforward, determining its volume requires a bit more precision. This article focuses on measuring the dimensions of bullion bars and coins to calculate their volume, which in turn allows us to determine their density. (There is another method to mesure density using Precious Metal Densimeter  which I will prenet in the next blog).

Measuring the Weight

The weight of the bullion can be easily measured using a high-precision scale. Ensure that the weight is recorded in grams for accuracy and consistency.

Measuring the Volume

To calculate the volume, we need to measure the dimensions of the bullion accurately. Most bullions come in the shape of either a rectangular bar or a round coin, and the formulas for their volumes are different.

Tools for Measuring Dimensions

To measure the dimensions accurately, we recommend using a digital caliper. Digital calipers are easy to use and provide precise

measurements, which are crucial for accurate volume calculations. When measuring, ensure that you select a point that best represents the dimension being measured to avoid any discrepancies.

Rectangular Bar

For a rectangular bar, the volume (V) is calculated using the formula:


  • 𝐴 and 𝐵 are the lengths of the vertices (base dimensions).
  • is the height of the bar.

Round Coin

For a round coin, the volume (V) is calculated using the formula:


  • is the diameter of the coin.
  • is the thickness of the coin.
  • 𝜋 (pi) is approximately 3.14.

Calculating Density

Once you have the weight in grams and the volume in cubic centimeters (cm³), you can calculate the density (ρ) using the formula: 𝜌=


  • Weight is in grams (g).
  • Volume is in cubic centimeters (cm³).

Confirming Authenticity

After calculating the density, compare it with the theoretical density of the metal. For instance, the theoretical density of pure gold is approximately 19.32 g/cm³, and for pure silver, it is approximately 10.49 g/cm³. If the calculated density closely matches the theoretical density, the bullion is likely to be authentic. This method is crucial because most assay tools only analyze the surface, whereas density provides information about the bulk material.

Special Note on Gold Coins

For certain gold coins such as the American Eagle, Krugerrand, Maple Leaf, Chinese Panda, and Buffalo, there is a specific tool known as the “Gold Coin Balance.” This mold helps confirm the density of these coins by ensuring they fit perfectly into the mold, which indirectly verifies their density and authenticity.


Measuring the dimensions of bullion accurately and calculating its density is an essential practice in the precious metals industry. By using digital calipers for precise measurements and comparing the calculated density with the theoretical density, one can verify the authenticity of the bullion. This method complements surface assays and provides a comprehensive analysis of the bullion’s composition.