Excavation
Bank volume = 160.00 m³
160.00 m³ × 1.25 swell = 200.00 m³ loose
160.00 m³ × 1.60 t/m³ = 256.00 t
Fill, trucks & cost
How it's calculated
V = L × W × DV = D × (L W + s D (L + W) + 4/3 s² D²)V = L × D × (W + s D)V = π d² D / 4V_loose = V_bank × (1 + swell %)M = V_bank × bank densityV_bank,fill = V_compacted / (1 − shrinkage %)⌈ V_loose / truck capacity ⌉Soil exists in three states. Bank volume is the soil in the ground, which is what the geometry gives. Loose volume is what you haul: dug soil takes more room, by the swell percentage.Compacted volume is the soil once it is placed and compacted as fill, which takes less room than it did in the ground, by the shrinkage percentage. A pit with sloped sides is a frustum, and the formula above is exact when all four sides have the same slope s (horizontal run for each 1 of depth). A trench with sloped sides has a trapezoid cross-section. Weight uses the bank density, because it is the mass of the soil that was in the ground. After digging, the base of the hole often takes a sub-base: see thegravel calculator; for footings and slabs, theconcrete calculator.
Worked example: a sloped pit
A pit with a base of 10 × 8 m, 2 m deep, with sides at 1:1 (45°), in common earth: bank density 1.60 t/m³, swell 25%, and a 10 m³ truck.
| Step | Working | Result |
|---|---|---|
| Top of the pit | (10 + 2 × 2) × (8 + 2 × 2) | 14 × 12 m |
| Bank volume | 2 × (80 + 1 × 2 × 18 + 4/3 × 1 × 4) | 242.67 m³ |
| Loose volume | 242.67 × 1.25 | 303.33 m³ |
| Weight | 242.67 × 1.60 | 388.3 t |
| Truck loads | ⌈ 303.33 / 10 ⌉ | 31 loads |
With vertical sides the same pit is 10 × 8 × 2 = 160 m³ bank, 200 m³ loose and 20 loads. A trench 50 m long, 0.6 m wide and 1.2 m deep is 36 m³ with vertical sides and 72 m³ if the sides slope at 0.5:1, because the section widens to 1.2 m at the top.
Assumptions
- Soil densities, swell and shrinkage are typical values from earthmoving references. They vary with moisture, grading and how well the soil is compacted. Edit them when you know your soil.
- Side slopes are the same on every side of a pit, and the ground is level. Uneven ground and stepped digs are not modelled.
- Sloped sides on a round pit are not modelled. Use a pit or the known-area shape.
- Weight is bank density times bank volume. Wet soil is heavier.
- Safe slopes, benching and shoring are not checked. Excavations deeper than about 1.2 m (UK practice) or 5 ft (OSHA) need support or a risk assessment before anyone goes in.
- Dewatering, breaking out hard material, tipping charges and haul distance are not included.
Frequently asked questions
What is the difference between bank, loose and compacted volume?
Bank is the soil in the ground, loose is the same soil after digging (larger), and compacted is the soil placed and compacted as fill (smaller than bank). A truck is filled with loose soil, so count trucks from the loose volume.
How much does soil swell when dug?
Typically 10 to 15% for sand and gravel, about 25% for common earth, 30% for clay, and more for blasted rock. The calculator uses 25% for common earth. Change it to match your soil.
How many truck loads is my excavation?
Divide the loose volume by the truck capacity and round up. A common tipper carries about 10 m³ (13 yd³) of loose soil, but check the payload as well: a wet, dense soil can reach the weight limit before the body is full.
How do I calculate a trench?
Length × depth × width for vertical sides. If the sides slope, use the bottom width plus the slope times the depth: V = L × D × (W + s × D).
What side slope should I use?
It depends on the soil, the depth, water and whether anyone works in the excavation. The calculator takes the slope you give it and does not judge whether it is safe. Ask a competent person to set the slope or the support.
What are OSHA soil types A, B and C?
OSHA 29 CFR 1926 Subpart P classes soil by strength: Type A is cohesive and the most stable (maximum slope 3/4:1), Type B is medium (1:1) and Type C is the weakest, such as sand, gravel and wet soil (1½:1). Slopes are given as horizontal to vertical, which is the same convention as the side slope field here. A competent person must classify the soil on site, so use these as a guide, not a design.
How much does a cubic metre of soil weigh?
About 1.4 to 1.8 tonnes in the ground, depending on the soil. Loose soil weighs less per cubic metre, because the same mass takes more room.
Standards and references
- BS 6031: code of practice for earthworks.
- BS EN 1997 (Eurocode 7): geotechnical design.
- OSHA 29 CFR 1926 Subpart P: excavations.
- Specification for Highway Works, Series 600: earthworks.
These documents cover the design and safe working of earthworks. The soil values used here are typical figures, not values from the standards. This calculator estimates quantities only. It does not check slope stability, shoring or ground conditions. Have the work designed and supervised by a competent person.