Applied Workshop Calculations (length, area, volume, mass, density)
Workshop calculations convert a drawing into material quantity. The chain is length to area to volume to mass using density. Keep every dimension in the same unit before calculating.
Core rules
- Area: rectangle l × b; circle πd²/4; triangle ½bh; trapezium ½(a + b)h.
- Volume: prism = area × length; cylinder = πd²/4 × h; cone = ⅓πr²h; sphere = 4/3πr³.
- Mass = volume × density. Typical densities: mild steel 7850 kg/m³ (7.85 g/cm³), cast iron 7200, aluminium 2700, copper 8900, brass 8500.
- Convert mm to m by dividing by 1000; mm³ to m³ by dividing by 10⁹.
Worked example
An MS plate is 1.2 m × 0.6 m × 10 mm. Thickness = 0.010 m. Volume = 1.2 × 0.6 × 0.010 = 0.0072 m³. Mass = 0.0072 × 7850 = 56.52 kg. If 8% is lost as scrap and offcuts, required mass = 56.52 × 1.08 = 61.04 kg. At ₹75/kg, material cost = ₹4,578.
Traps
- Mixing mm and m in the same formula.
- Using diameter as radius.
- Treating 7.85 g/cm³ and 7850 kg/m³ as different densities; they are the same.
- Forgetting the scrap allowance when ordering material.
- Rounding the volume too early, before multiplying by density.