Volume & metal pricing calculator
How Katura computes piece weight from STL geometry and live spot prices.
Overview
Once an STL is watertight, Katura can compute the piece's volume to high precision. Multiply that by the alloy density, and you have grams. Multiply grams by the live metal spot price (plus your studio's alloy / labor / margin multipliers), and you have a quote that updates the moment the market moves.
The formula in plain English
- Volume (cm³) = sum of signed-tetrahedron volumes for every triangle in the mesh.
- Mass (g) = volume × alloy density (e.g. 14k yellow gold ≈ 13.07 g/cm³).
- Metal cost = mass × spot price ÷ 31.1035 (grams per troy ounce).
- Studio cost = metal cost ×
alloyMultiplier+ flatlaborCost+ per-stone setting fees. - Customer price = studio cost ×
marginMultiplier, rounded to your studio's pricing rules.
Built-in alloy densities
| Alloy | Density (g/cm³) |
|---|---|
| 14k yellow gold | 13.07 |
| 14k white gold | 12.61 |
| 14k rose gold | 13.00 |
| 18k yellow gold | 15.58 |
| Platinum 950 | 20.10 |
| Sterling silver 925 | 10.36 |
| Palladium 950 | 11.90 |
You can override any of these per-studio in /admin/settings/cad.
Studio multipliers
Most studios end up with three knobs:
- Alloy multiplier — accounts for casting waste, refining loss, and the cost of finishing alloy you have to buy at retail.
- Labor flat — bench time, polishing, QA. Often broken out per piece-type.
- Margin multiplier — your wholesale or retail markup.
Tip
Volume is computed once on upload and cached. Recomputing happens automatically when you replace the STL or change the alloy. The math is fast (<100ms for typical jewelry meshes) but the cache keeps page renders snappy.
Worked example
For our Homage ring:
- Volume: 0.42 cm³
- Alloy: 14k yellow gold (13.07 g/cm³)
- Mass: 5.49 g
- Spot price: $2,650 / troy oz
- Metal cost: 5.49 × 2,650 / 31.1035 = $467.66
- With 1.4× alloy + $180 labor + 2.2× margin: ≈ $1,795 retail