Metal weight calculator

The band's volume

A band is a cross-section swept once around the finger, so its volume is the area of that cross-section times the distance its centre travels (Pappus's theorem). For a flat band that comes to π × (outer radius² − inner radius²) × width. A D-shape is flat inside and half round outside: its cross-section is half an ellipse, π × width × thickness ÷ 4, and its centre sits 4 × thickness ÷ 3π out from the inside. Comfort-fit (court) bands, rounded on both sides, fall between the two.

A worked example

A flat band 17.3 mm inside, 4 mm wide and 1.8 mm thick has an inner radius of 8.65 mm and an outer radius of 10.45 mm. Its volume is π × (10.45² − 8.65²) × 4 = 432 mm³, or 0.432 cm³. In 18k yellow gold at 15.5 g/cm³ that weighs 0.432 × 15.5 = 6.70 g (4.31 dwt); in platinum 950 at 21.4 g/cm³, 9.25 g. The same size as a D-shape holds 334 mm³, about 23% less metal.

For any other design

Choose The metal volume and enter the volume of the metal parts in mm³. In Rhino, the Volume command measures a closed polysurface or mesh. In Jart, open the file and Design Facts measures every metal part from the mesh and weighs it in its own metal and the six alloys jewellers usually quote in. Either way the shape must be closed: a mesh with holes has no true volume.

What the number leaves out

This is the weight of the finished metal. Your caster adds the sprue and the metal lost in casting and finishing, and refiners' alloys differ by a few percent, so ask yours for their figures before you quote. Stones are not included: a set stone replaces metal, so measure the metal parts alone. One pennyweight (dwt) is 1.55517384 g.