Backfill Calculator

How much backfill do I need?

This backfill calculator takes the volume of your trench, subtracts the space the buried pipe will occupy, and gives you the soil needed to fill what remains. The formula is backfill = trench volume − (π × pipe radius² × pipe length), with the pipe radius converted from inches to feet. A 300 ft³ trench holding 100 ft of 8-inch pipe needs 265 ft³ of backfill, or 9.82 cubic yards.

Enter the trench volume in cubic feet, the pipe diameter in inches, and the pipe length in feet. You get backfill in cubic yards, which is how soil and gravel are usually sold, and in cubic feet.

The formula in plain words

A pipe is a long cylinder, so its volume is the area of its circular end times its length.

1. Pipe radius in feet = diameter in inches ÷ 2 ÷ 12. An 8-inch pipe has a radius of 0.333 ft.
2. Pipe volume = π × radius² × length. For 100 ft of 8-inch pipe: 3.1416 × 0.111 × 100 = 34.91 ft³.
3. Backfill = trench volume − pipe volume, never less than zero.
4. Cubic yards = backfill cubic feet ÷ 27.

If you only know the trench dimensions, multiply length × width × depth in feet first. The trench volume calculator does that step for you.

Worked examples

1. Storm line: 300 ft³ trench, 8-inch pipe, 100 ft long

• Pipe volume: π × (0.333)² × 100 = 34.91 ft³
• Backfill: 300 − 34.91 = 265.09, shown as 265 ft³
• Cubic yards: 265.09 ÷ 27 = 9.82 yd³

2. Culvert crossing: trench 60 ft × 2 ft × 4 ft, 12-inch pipe, 60 ft long

• Trench volume: 60 × 2 × 4 = 480 ft³
• Pipe volume: π × (0.5)² × 60 = 47.12 ft³
• Backfill: 480 − 47.12 = 432.88, shown as 433 ft³
• Cubic yards: 16.03 yd³

Neither figure includes compaction. If the backfill is tamped in lifts, order more loose material than these numbers show.

How much space each pipe size takes

Pipe diameter	Volume per foot (ft³)	Volume per 100 ft (yd³)
4 in	0.087	0.32
6 in	0.196	0.73
8 in	0.349	1.29
12 in	0.785	2.91
15 in	1.227	4.55
18 in	1.767	6.54
24 in	3.142	11.64
36 in	7.069	26.18

For small drain and water lines the correction is tiny, and you could skip it. For culverts and sewer mains it can take several truckloads off the order.

How to measure a trench for backfill

• Measure depth at several points. Trench bottoms are rarely level. Take a depth reading every 10 ft or so and use the average.
• Measure width at the bottom and the top. If the walls slope or are benched for safety, average the two widths. Sloped trenches hold far more soil than vertical-wall trenches of the same depth.
• Use the pipe’s outside diameter. Pipes are sold by nominal (inside) size. The wall and any bell joints make the outside larger. That difference matters most for thick concrete pipe.
• Subtract bedding separately. If the spec calls for a stone or sand bed and haunch zone, calculate that layer on its own. The rest is general backfill.

Common backfill mistakes

• Ordering the bank volume. Soil swells when dug and shrinks when compacted. The exact hole volume is rarely the exact truck volume. Use the fill dirt compaction calculator to convert compacted cubic yards into loose yards to order.
• Dumping it all in at once. Backfill placed in one deep pour settles for months and leaves a sunken strip. Place and compact it in thin lifts, commonly 6 to 12 inches, as the spec requires.
• Rocks against the pipe. Large stones in the first layer can crack plastic pipe or point-load it. Use screened or select material around the pipe and save the rocky spoil for higher up.
• Forgetting spoil you will haul away. If the excavated soil cannot be reused, plan for both importing backfill and removing spoil. The cut and fill calculator helps balance the two.

This is a planning estimate. Pipe bedding, compaction lifts, and backfill material are often set by the project engineer or local utility, so check those specs before you order.