Trench calculator: excavation, bedding and backfill

Bank cubic yards per linear foot for a trench 3 feet wide at the bottom, by depth to the bottom of the trench and by wall. Sloped walls grow with the square of the depth, which is why a deep Type C trench is so much more dirt than the same trench in a box.

Multiply by the length for bank yards; the calculator handles a run whose depth changes.

Stone in place per 100 feet of pipe, in a trench the pipe's outside diameter plus 2 feet wide, with 6 inches under the pipe. The pipe's own volume is taken out; some free calculators skip that, which overstates the stone more the bigger the pipe. Tons at 1.42 tons per cubic yard.

In a sloped trench the stone zone widens with the slope; the calculator accounts for it.

1. Depth actually dug. The plans give depth to the invert, the inside bottom of the pipe. The trench goes deeper by the pipe's wall, (O.D. − I.D.) ÷ 2, and by the bedding under it.
2. Excavation. A trench b feet wide at the bottom with sides at m:1 has a section of b × D + m × D². When the depth runs from D₁ to D₂ along the run, D² averages (D₁² + D₁D₂ + D₂²) ÷ 3, so volume = length × (b × average depth + m × that average). Averaging the two end sections instead overstates a sloped trench.
3. Stone. The zone from the trench bottom up to the springline, or over the top of the pipe, is b × z + m × z² in section. The pipe's area, π ÷ 4 × O.D.², comes out of it (half of it, to the springline).
4. Backfill. The excavation less the stone and the pipe, placed and compacted. Compacted yards ÷ the bank-to-compacted factor is the bank dirt it takes.
5. Left over. Bank yards dug less the bank yards the backfill takes. Negative means the trench needs borrow. The soil converter explains the factors, and the haul calculator turns what's left into loads.

Site Bid prices trench excavation the same way, structure to structure, by the depth each run is actually dug.

300 feet of 8-inch PVC sewer (O.D. 8.4 in), 7 to 9 feet to invert, in dry clay sloped for Type B soil (1:1), with a bottom width of 2.7 feet, 6 inches of bedding and stone 12 inches over the pipe:

• Dug 7.52 to 9.52 feet deep, 17.7 to 21.7 feet wide at the top.
• Excavation 1,066 bank yards (1,524 loose).
• Stone 115.5 yards in place, 164 tons.
• Backfill 946 compacted yards, taking 1,051 bank yards.
• Left over: 15 bank yards, 21 loose to haul.

In a trench box 2.7 feet wide, the same run digs 256 bank yards, 24% of the sloped trench.

• Maximum allowable slopes for excavations under 20 feet (29 CFR 1926 Subpart P, Appendix B, Table B-1): stable rock vertical, Type A ¾:1, Type B 1:1, Type C 1½:1. Type A may go to ½:1 for no more than 24 hours in excavations 12 feet deep or less.
• No soil is Type A if it's fissured, subject to vibration, or previously disturbed. Submerged soil, or soil with water seeping from it, is Type C (Appendix A).
• Trenches 5 feet or deeper need a protective system unless they're entirely in stable rock; under 5 feet, none is needed only if a competent person finds no indication of a possible cave-in (1926.652(a)(1)(ii)). Anything over 20 feet needs a system designed by a registered professional engineer.
• Without classifying the soil, slopes may be no steeper than 1½:1.

• OSHA, 29 CFR 1926 Subpart P, Appendix B, Appendix A and 1926.652. Checked October 3, 2026.
• Trench width example: NCDOT Roadway Standard Drawing 300.01, Method of Pipe Installation (2024). connect.ncdot.gov. Checked October 3, 2026.
• PVC sewer outside diameters: ASTM D3034, as listed by Porter Pipe. Source. Checked October 3, 2026.
• HDPE outside diameters: ADS N-12 WT IB (AASHTO) specification. Source. Checked October 3, 2026.
• Ductile iron sections: DIPRA, Thrust Restraint Design for Ductile Iron Pipe, Table 2. Source. Checked October 3, 2026.
• RCP outside diameters use the Wall B rule (wall in inches = diameter in feet + 1) from secondary sources and are approximate; check them against your supplier's sheet.
• Soil factors: US Army FM 5-434, Earthmoving Operations (2000), Tables 1-1 and 1-2. Read the manual.

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