A pipe occupies part of a trench that would otherwise contain fill. For a straight, rectangular trench with one circular pipe along its full length, subtract the pipe’s exterior cylinder from the trench volume.

Formula: net ft³ = length × width × depth − π × (outside diameter in inches ÷ 24)² × length; yd³ = ft³ ÷ 27

Worked example

For a 100 ft long, 3 ft wide, 4 ft deep trench with a 12 in outside-diameter pipe, the trench is 1,200 ft³ and the pipe occupies about 78.54 ft³. Net fill space is about 41.54 yd³.

Use outside diameter

Nominal pipe size and inside diameter may differ from the exterior dimension. Fill cannot occupy the pipe wall or its interior, so the displaced cylinder uses the actual outside diameter. A zero diameter gives the rectangular trench volume without a pipe subtraction.

This is an idealized shape

The calculation assumes vertical sides, uniform width and depth, and one fully enclosed pipe for the entire length. Sloped walls, structures, multiple pipes, joints and partial runs require separate geometry. INDOT’s backfill examples illustrate why real project sections and prescribed fill zones can be more detailed than this simple estimate.

Net space is not loose delivery volume

The result includes all geometric space outside the pipe, without separating bedding, pipe-zone fill or reused soil. It does not add waste, settlement, compaction or excavation swell. Use the bulk-density guide only after identifying the material state and the quantity you actually plan to purchase.

Explore the related calculation

For a different starting point, try the bulk-density guide or return to the main calculator. Browse the complete tool directory for this site.

Reference and corrections

The definitions and assumptions above follow these sources; the examples and calculator arithmetic are original to this page.

www.in.gov reference

Found a problem? Email contact@cubicyardstotons.org.

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