A 100 ft long, 6 ft deep trench with a 4 ft bottom holds 288.89 yd³ of bank soil under a Type C slope of 1.5:1. Every step that produces that number is checkable: set the slope ratio, find the top width, compute the cross-section, extend the section into a bank volume, and convert it to loose volume only with a project-specific factor. The Sloped-Trench Excavation Calculator repeats this calculation for any length, bottom width, depth, and slope ratio you enter.
What trench does this example use?
The example trench is 100 ft long with a uniform section, 6 ft deep, and 4 ft wide at the bottom. The soil is Type C, so OSHA Table B-1 allows a maximum slope of 1.5 horizontal to 1 vertical for an excavation under 20 ft deep. The section has no benching, no rock, and no standing water.
How do you turn the slope ratio into a top width?
A 1.5:1 slope means each wall moves 1.5 ft horizontally for every 1 ft of depth. Multiply by the depth: 1.5 × 6 = 9 ft of horizontal offset per side. Add both sides to the bottom width: 4 + 2 × 9 = 22 ft top width.
The OSHA ratio 1.5:1 reads as horizontal:vertical. Measuring the angle from the horizontal flips the ratio and produces a wall far steeper than the soil allows.
How do you get the cross-section from the top width?
The trench section is a trapezoid. Its area is (bottom width + top width) ÷ 2 × depth: (4 + 22) ÷ 2 × 6 = 13 × 6 = 78 ft².
How does the section become a bank volume?
Multiply the section area by the trench length: 78 × 100 = 7,800 ft³. Divide by 27 for cubic yards: 7,800 ÷ 27 = 288.89 yd³. This is the bank volume, the soil measured in place before digging. Record the state beside the number.
How do you convert bank volume to loose volume?
Excavation loosens the soil, so the loose volume is larger. Multiply the bank volume by a swell factor from the project record or an approved reference table. With an example-only factor of 1.25: 288.89 × 1.25 = 361.11 yd³ loose.
Swell depends on the soil, the equipment, and the moisture. Use a factor measured on your material or taken from a reference your project accepts, and keep bank and loose volumes labeled separately as the bank vs loose volume guide shows.
How do you check the backfill quantity?
Backfill is the bank volume minus the volume the pipe or structure displaces. A 12-inch (1 ft diameter) pipe running the full 100 ft displaces π × 0.5² = 0.7854 ft² of section, or 78.54 ft³ = 2.91 yd³. Backfill = 288.89 − 2.91 = 285.98 yd³ in the bank state. Bedding, compaction, and settlement allowance are separate project decisions, not part of this subtraction.
| Step | Computation | Result |
|---|---|---|
| Slope offset per side | 1.5 × 6 ft | 9 ft |
| Top width | 4 + 2 × 9 ft | 22 ft |
| Section area | (4 + 22) ÷ 2 × 6 ft | 78 ft² |
| Bank volume | 78 × 100 ft³ ÷ 27 | 288.89 yd³ |
| Loose volume (example factor 1.25) | 288.89 × 1.25 | 361.11 yd³ |
| Pipe displacement | π × 0.5² × 100 ft³ ÷ 27 | 2.91 yd³ |
| Backfill quantity | 288.89 − 2.91 | 285.98 yd³ |
What changes when the soil is Type A?
Run the same five steps with the Type A slope of 0.75:1. The offset per side is 0.75 × 6 = 4.5 ft, the top width is 4 + 9 = 13 ft, and the section area is (4 + 13) ÷ 2 × 6 = 51 ft². Bank volume = 51 × 100 = 5,100 ft³ = 188.89 yd³. The soil classification alone creates a 100 yd³ gap, which is why soil classification sets the slope ratio before any ordering.
How does the same example work in metric?
Take a 30 m long trench, 1.8 m deep, 1.2 m bottom width, in Type B soil with a 1:1 slope. Offset per side = 1 × 1.8 = 1.8 m. Top width = 1.2 + 3.6 = 4.8 m. Section area = (1.2 + 4.8) ÷ 2 × 1.8 = 5.4 m². Bank volume = 5.4 × 30 = 162 m³. With an example-only swell factor of 1.30, the loose volume is 162 × 1.30 = 210.6 m³.
Safety and professional scope
In the U.S., OSHA requires a protective system such as sloping for excavations 5 ft or deeper, and sloping for excavations deeper than 20 ft must be designed by a registered professional engineer. The slope ratios in this example are maximum allowable values under OSHA Table B-1, not substitutes for the project safety plan, a competent person’s soil classification, or the geotechnical drawings.
Sources and scope
- OSHA 29 CFR 1926 Subpart P, Appendix B, Table B-1: maximum allowable slopes (Stable rock vertical, Type A 3/4:1, Type B 1:1, Type C 1½:1), accessed 2026-10-16: https://www.osha.gov/laws-regs/regulations/standardnumber/1926/1926subpartpappb
- OSHA 29 CFR 1926.652: protective systems for excavations 5 ft or deeper, accessed 2026-10-16: https://www.osha.gov/laws-regs/regulations/standardnumber/1926/1926.652
Scope: this article works through a sloped-trench quantity takeoff with fixed example dimensions. The governing drawings, geotechnical information, survey and testing methods, contract measurement rules, and safety controls for your project take precedence over these example numbers.
Next, review the common sloped-trench mistakes to see how each error changes the quantity, or see how to measure a sloped trench before you compute. For volume ordering, use the Earthwork & Drainage Calculators hub.
