How this calculator works
Choose a solid geometry or enter measured volume or mass. A ring is treated as a circular torus; a tube or bead uses an annular cylinder. Pure-metal reference densities are at room temperature. Karat describes gold mass fraction, not alloy density: yellow, rose and white alloys at the same karat can have different densities. Enter an alloy datasheet value for jewellery. The price is a user-supplied amount per gram, with allowance added to finished mass; it is not a live gold quote.
Formula
m = rho V; torus V = 2 pi^2 R r^2; tube V = pi (Ro^2 - Ri^2) L; stock mass = finished mass (1 + allowance/100).
Worked example
A pure-gold sheet 20 mm by 10 mm by 1 mm has volume 0.2 mL and mass 3.86 g. At $100/g with 10% extra material, estimated material cost is $424.60.
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Frequently asked questions
Can I multiply pure gold density by karat fraction?
No. Alloying metals also occupy volume. Use the density of the particular jewellery alloy.
Is cost a live market price?
No. Enter the price you intend to use. Labour, taxes and fabrication charges are excluded.
Does allowance mean loss from purchased stock?
Here allowance is extra material as a percentage of finished mass. A yield percentage would require a different calculation.