Trench calculator
Show the working — with your numbers
These are volumes from the box you describe and the depths you type. Ground conditions, water and the way the spoil breaks up all change the real figures, so treat the spoil and tonnage as haulage estimates. The tool says nothing about shoring, trench safety, a safe slope, the required cover, or whether a pipe may be bedded in a given material — those are your spec, your code and a competent person on site.
Enter the trench length, width and depth, the pipe's outside diameter and the bedding you have been told to put under and over it, and the tool gives you the dig in cubic yards or metres, the loose spoil to haul after swell, the bedding volume (with tonnage if you type a density), and the backfill left to bring the trench back to grade. Every one of those is arithmetic on your numbers; the depths that matter to the pipe are yours to enter, not this page's to suggest.
Worked example
A 100 ft run, 24 in wide, 4 ft deep, carrying a 6 in pipe on 4 in of sand with 6 in of cover, in ground that swells 25%. The dig is 100 × 2 × 4 = 800 ft³, which is 800 ÷ 27 = 29.6 yd³ bank. The spoil is 29.6 × 1.25 = 37.0 yd³ loose. The bedding envelope is 4 + 6 + 6 = 16 in = 1.333 ft tall, so 100 × 2 × 1.333 = 266.7 ft³, less the pipe (π × 0.25² × 100 = 19.6 ft³) is 247.0 ft³ = 9.15 yd³ of bedding; at a pit density of 1.4 t/yd³ that is about 12.8 tons. What is left above the envelope is 4 − 1.333 = 2.667 ft, so 100 × 2 × 2.667 = 533.3 ft³ = 19.8 yd³ of backfill. The three pieces — bedding, backfill and the pipe — add back up to the 800 ft³ dig.
The same in metric: a 30 m run, 600 mm wide, 1.2 m deep, carrying a 150 mm pipe on 100 mm of sand with 150 mm of cover, 25% swell. The dig is 30 × 0.6 × 1.2 = 21.6 m³ bank, and the spoil 21.6 × 1.25 = 27 m³ loose. The envelope is 100 + 150 + 150 = 400 mm = 0.4 m, so 30 × 0.6 × 0.4 = 7.2 m³, less the pipe (π × 0.075² × 30 = 0.53 m³) is 6.67 m³ of bedding; at 1.66 t/m³ that is about 11.1 tonnes. Above the envelope 0.8 m is left: 30 × 0.6 × 0.8 = 14.4 m³ of backfill.
On the job
Where the surplus goes. Backfill with the native spoil and you will not use it all: the bedding and the pipe have taken the bottom 16 inches of the trench. In the example that is 800 − 533 = 267 ft³ of bank soil with nowhere to go, and once it has swelled it is 267 × 1.25 = 333 ft³ — about 12.4 loose yards to truck off, before you count the spoil that never compacts back down. Price the haul off that figure, not off the whole dig. (In the metric example: 21.6 − 14.4 = 7.2 m³ bank, 9 m³ loose.)
Bedding by the ton. The pit sells sand and clear stone by weight. The density field turns the bedding volume into tons using the pit's own number — ask for it, because clear stone and screened sand are not the same weight per yard. Bedding is placed and compacted in lifts, and the compacted volume is less than the loose volume delivered; if your supplier gives a compaction allowance, add it to the depth you type rather than trusting a rule of thumb.
A conduit bank, not one pipe. Three 4 in conduits side by side do not have one diameter. Put in the height of the bank (one conduit, 4 in, if they lie in a single row) for the envelope, and accept that the displaced-pipe figure is slightly low — three round conduits displace a little more than one. On a small bank the difference is a fraction of a yard; on a big duct bank, run the envelope as a plain box with the pipe diameter at zero and subtract the ducts by hand.
What went wrong?
Quick referencefor a trench
- Dig (bank)
- length × width × depth · ft³ ÷ 27 = yd³
- Spoil (loose)
- bank × (1 + swell%) — the pile is bigger than the hole
- Bedding envelope
- below + pipe OD + cover, × width × length, less the pipe
- Pipe volume
- π × (OD ÷ 2)² × length
- Backfill
- width × (depth − envelope) × length
- Tons of bedding
- yd³ × the pit's density (t/yd³)
- Metric
- 1 m³ = 1.31 yd³ · 1 tonne = 1.10 short tons · 1 in = 25.4 mm
- Dig in metric
- length × width × depth in metres = m³ · mm ÷ 1,000 first
- Density
- 1 ton per yd³ = 1.19 tonnes per m³
Waste & overagewhat to add, and why
- Pipe crews order bedding 10–15% over because the trench bottom is never flat and the sand fills the low spots first; the bedding tonnage here is on the depths you typed, so the margin is yours to add.
- Spoil is booked on loose volume — the swell field starts at 25%, but stiff clay can swell more, and sand barely swells; ask the operator.
- If backfill is imported, order it compacted-in-place volume plus a margin, not loose — it goes in and gets tamped down.
Mistakes to catchbefore you order
- Typing the trench width at grade when the walls are battered — the volume is the average width, and a battered trench is wider than the bottom you dug for.
- Forgetting the pipe: on a big line the pipe volume is real backfill you do not need, and the tool subtracts it only if you type the outside diameter.
- Using the pipe's nominal size as its outside diameter; a 4 in pipe is bigger than 4 in outside.
What an inspector looks forthe utility or building inspector, with the safety officer alongside
On this part of the job
- Trench protection: slope, bench or shore for the depth and soil you are actually in, spoil back from the lip, and a way out. An inspector may stop the job for this before looking at anything else.
- Cover over the pipe or cable — measured from finished grade to the top of the service, against the depth the utility or the code requires. Look that figure up and type it into the tool; it varies by service and by jurisdiction.
- Bedding and haunching: the material specified, to the thickness specified, worked in under the haunches so the pipe is supported along its whole length and not bridging on lumps.
- Grade and fall of the pipe where it is a gravity line — checked with an instrument, not a level on a short straightedge.
- Warning tape or marker at the depth specified above the service, and any required separation from other utilities crossing or running parallel.
- Backfill in compacted lifts, and that no rock or frozen material went in against the pipe.
Have this ready
- Locate tickets and the as-built or servicing drawing.
- The bedding and cover specification for this service, printed.
- The trench open at the inspection point, safely, with the bedding still visible.
Every figure an inspector measures against comes from the code your jurisdiction has adopted, the stamped drawing, or the manufacturer's printed instructions — so none of them are printed here. Look the number up in your own book, type it into the tool, and the arithmetic is yours.
The formula
dig = L × W × D · bedding = L × W × (below + OD + cover) − π(OD/2)² × L · backfill = dig − bedding − pipe
Bring the width, the pipe and the bedding depths into feet (or metres) first, then work the three boxes: the whole dig, the bedding envelope at the bottom, and the backfill above it. The pipe volume comes off the envelope. Spoil is the dig multiplied by one plus the swell.
What this tool assumes
A trench with vertical sides and a flat bottom, one pipe or conduit of the diameter you give, and bedding that fills the width of the trench around it. The bedding and cover depths, the swell and the density are all your figures; the defaults for the trench itself are just a starting shape. Sloped or benched trench walls hold more than the box — add the extra by widening the width you type, or run the excavation calculator with its over-dig allowance for the dig alone.
Questions
- How do I calculate trench volume?
- Length × width × depth. A 100 ft trench, 2 ft wide and 4 ft deep is 800 cubic feet, which is 800 ÷ 27 = 29.6 cubic yards in the ground (22.7 m³). In metric, a 30 m trench 0.6 m wide and 1.2 m deep is 21.6 cubic metres. That is the bank volume — the dig. The spoil that comes out is bigger once it is broken up, and that is what the swell field adds.
- How much bedding sand or stone do I need for a pipe?
- Bedding fills the bottom of the trench below the pipe, wraps the pipe, and covers it to whatever depth your spec calls for — minus the pipe itself. Trench width × (bedding below + pipe diameter + cover above) × length gives the envelope, and the pipe volume comes off it. You enter the bedding and cover depths; they come from the utility, the engineer or the code, not from this page.
- What is the difference between bedding, backfill and spoil?
- Bedding is the imported material placed around the pipe. Backfill is what goes in above the bedding to bring the trench back to grade — often the native spoil, sometimes imported. Spoil is everything that came out of the hole; after swell it is more than the hole, and after the bedding has taken its share of the trench the surplus spoil has to go somewhere.
- Why is the backfill less than the dig?
- Because part of the trench is now full of pipe and bedding. The dig is the whole box; the bedding envelope takes the bottom of it; the backfill is only the depth left above the envelope. If you backfill with the native spoil you will have that envelope volume left over, swelled — which is the pile the truck takes away.
- How much does the soil swell?
- It depends on what you are digging. The default here is the same 25 percent the excavation page starts with, which is in the range for common earth; sand swells less, heavy clay and rock more. It is an editable field for exactly that reason — put in the figure your hauler or your experience gives you.
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