Formula and method
Volume in m³ = length × width × depth × allowance factor. Metric tonnes = volume × density in kg/m³ ÷ 1,000.
Worked example
A 5 m × 4 m area at 5 cm depth, with 10% extra, needs 1.1 m³. At 1,600 kg/m³ this is 1.76 metric tonnes.
Area shapes and roadway fill
Circular areas use π/4 × diameter² × depth and triangular areas ½ × base × height × depth. Roadway or trench fill multiplies length × width × compacted depth, then adds a compaction or cut-fill allowance for the extra loose material needed to reach that depth, before the ordering allowance.
Tonnes and short tons
Mass = volume × bulk density. Metric tonnes divide kilograms by 1,000; US short tons divide by 907.18474 (2,000 lb). Suppliers quote either unit, so check which one before comparing prices. Cost can be priced per short ton, tonne, cubic yard or cubic meter.
Worked example: roadway
A driveway base 100 ft long, 12 ft wide and 6 in deep is 600 ft³. With a 15% compaction allowance and the extra-material allowance set to 0%, that becomes 690 ft³, or 25.56 yd³. At 1,600 kg/m³ this is about 31.26 metric tonnes, or 34.46 US short tons. With the default 10% extra-material allowance the order is 759 ft³ (28.11 yd³), about 34.39 tonnes or 37.91 short tons.