The basic brass calculation formula (length × width × height in feet, divided by 100) is printed on every site diary. Real sites are rarely perfect boxes, though: trenches have sloping sides, sand is dumped in cones, and plots dip at one corner. This guide gives the formula for each shape a supervisor actually meets, with numbers worked through so they can be checked on a phone calculator.
The brass calculation formula behind every shape
Brass = Volume in cubic feet ÷ 100 Brass = Volume in cubic metres ÷ 2.832
Everything below is just a way of finding the volume. Measure in feet wherever possible and convert inches before multiplying: 6 inches is 0.5 ft, 9 inches 0.75 ft, 3 inches 0.25 ft.
1. Rectangular pits and footings
Brass = L × W × D ÷ 100 × number of pits
Twelve footing pits of 4 ft × 4 ft × 5 ft: 4 × 4 × 5 = 80 CFT each, × 12 = 960 CFT = 9.6 brass of excavation.
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2. Trenches with sloping sides
Trenches in loose soil are dug wider at the top for safety. The cross-section is a trapezium, so average the top and bottom widths:
Brass = Length × ((Top width + Bottom width) ÷ 2) × Depth ÷ 100
A 60 ft plinth trench, 3 ft wide at the bottom, 4 ft at the top and 4 ft deep: 60 × 3.5 × 4 = 840 CFT = 8.4 brass. Using the top width alone would have billed 9.6 brass, 14% too much.
How do I measure the length of trenches for a whole building?
Use the centre-line length: add up the centre lines of all walls. Measuring outside lengths counts every corner twice.
3. Heaps of sand, gitti and murum
Round (conical) heap
Volume = π × r² × h ÷ 3 (r = radius at the base, h = height)
A cone of sand 12 ft across (r = 6 ft) and 4 ft high: 3.1416 × 36 × 4 ÷ 3 ≈ 151 CFT = 1.5 brass. To find the radius, walk around the heap with a tape: circumference ÷ 6.283.
Long heap along a road (a ridge)
A long heap has a roughly triangular cross-section:
Volume = Length × Base width × Height ÷ 2
A ridge of murum 40 ft long, 8 ft wide at the base and 3 ft high: 40 × 8 × 3 ÷ 2 = 480 CFT = 4.8 brass. A heap with a flattened top holds more; treat it as a trapezium instead (average of top and base widths).
Heaps on soft ground sink a few inches into it, and the edges spread. Measuring a heap is always a rough check; the levelled truck body before tipping is the fair measurement.
4. Round pits, wells and sumps
Volume = π × r² × D
A soak pit 5 ft across and 8 ft deep: 3.1416 × 2.5² × 8 ≈ 157 CFT = 1.57 brass of earth removed.
5. Uneven plots: the average depth method
For levelling or filling a plot whose ground isn't flat, surveyors take depths at several points on a grid and average them:
- Stretch strings to divide the plot into equal squares (for example every 10 ft).
- At each grid point, measure how much fill (or cut) is needed to reach the final level.
- Average all the readings, then multiply by the plot area.
A 50 ft × 40 ft plot with readings of 1.0, 1.5, 2.0, 1.2, 0.8 and 1.5 ft average 8 ÷ 6 = 1.333 ft. Volume = 2,000 × 1.333 ≈ 2,667 CFT = 26.7 brass, plus about 10–15% for compaction.
Allowances that change the order
| Situation | Why | Typical allowance |
|---|---|---|
| Excavated earth for transport | Dug soil loosens (bulking) | +20 to 30% |
| Filling that will be compacted | Material settles when rolled and watered | +10 to 15% |
| Damp sand | Bulking makes it occupy more space | Buy by weight or check moisture |
These are planning figures; soil type and moisture change them, so a site engineer's judgement on the day matters.
Frequently asked questions
What is the brass calculation formula?
Brass = length × width × height in feet ÷ 100, or cubic metres ÷ 2.832.
How do I calculate brass for a trench with sloping sides?
Multiply length × average of top and bottom widths × depth, then divide by 100.
How do I calculate brass of a sand heap?
For a round heap use π × r² × h ÷ 3; for a long ridge use length × base width × height ÷ 2. Divide the cubic feet by 100.
How do I calculate brass for filling an uneven plot?
Take fill depths at grid points, average them, multiply by the plot area and divide by 100. Add 10–15% for compaction.
How many cubic metres is 1 brass?
2.832 cubic metres.
Keep reading
- Brass Volume Calculator: the free tool this guide explains.
- All construction calculators
- 1 Brass in Kg, Sq Ft and CFT: A Site Buyer's Cheat Sheet
Sources: standard mensuration formulas (prism, frustum, cone, cylinder); 1 brass = 100 ft³ = 2.832 m³.