Excavation calculator

Bank volume, loose volume and truck loads — with the swell the material actually has.

Units

Swell decides how many truck loads leave the site. The percentages are the US Army's published figures, not ours.

Sloped sides and hauling

Zero for vertical walls. Cut back at 1:1 and the hole holds far more than the box you measured.

Optional. Loads are counted on the loose volume, which is the only volume a truck body sees.

Enter the size of the hole to see the volume in the ground and in the truck.

    The hole is not the pile

    Dig a cubic yard out of the ground and you do not have a cubic yard of dirt. You have between 1.1 and 1.65 cubic yards, depending on what it was, because excavating opens voids that the ground's own weight had closed. That expansion is called swell, and it is the difference between the volume you calculated and the volume you are billed to take away.

    bank yd³ = L × W × D ÷ 27 (the hole) loose yd³ = bank × (1 + swell%) (the pile) 20 × 10 × 4 ft of dry earth bank 29.63 yd³ swell 15–35% loose 34.07 – 40 yd³ In a 10 yd³ truck: 4 loads. The bank figure alone says 3.

    One swell factor for everything is wrong

    Most excavation calculators apply a single number — usually 25 percent — to whatever you are digging. The manual these figures come from lists eleven materials spanning 10 percent to 65. Dry sand swells a tenth. Dry clay swells two fifths. Shale swells nearly two thirds. On the same 20 by 10 foot hole, clay produces 41.48 loose yards where dry earth at the bottom of its band produces 34.07.

    Swell, load factor and weight by material

    MaterialSwellLoad factorLoose weight per yd³Bank weight per yd³
    Cinders40–55%0.65–0.72800–1,200 lb1,100–1,860 lb
    Clay, dry40%0.721,700–2,000 lb2,360–2,780 lb
    Clay, wet40%0.722,400–3,000 lb3,360–4,200 lb
    Earth (loam or silt), dry15–35%0.74–0.871,900–2,200 lb2,180–2,980 lb
    Earth (loam or silt), wet25%0.82,800–3,200 lb3,500–4,000 lb
    Gravel, dry10–15%0.87–0.912,700–3,000 lb2,980–3,450 lb
    Gravel, wet10–15%0.87–0.912,800–3,100 lb3,080–3,560 lb
    Sand, dry10–15%0.87–0.912,600–2,900 lb2,860–3,340 lb
    Sand, wet10–15%0.87–0.912,800–3,100 lb3,080–3,560 lb
    Shale (soft rock)65%0.62,400–2,700 lb4,000–4,500 lb
    Traprock50%0.662,700–3,500 lb4,100–5,300 lb

    US Army FM 5-434, Table 1-2. Public domain. Bands are the manual's own — it publishes no midpoints, and neither does this page.

    Bank, loose and compacted

    Three measurements of one pile of dirt, and the reason earthworks quotations argue. Bank is the material in the ground — the size of the hole. Loose is after digging, and it is bigger. Compacted is after placing and rolling, and it is usually smaller than bank. A supplier quotes loose. A drawing specifies compacted. Neither says which, and the gap between them for clay is more than a factor of two.

    Converting between the three states

    MaterialBank → looseBank → compactedLoose → bankCompacted → loose
    Sand or gravel× 1.11× 0.95× 0.9× 1.17
    Loam (common earth)× 1.25× 0.9× 0.8× 1.39
    Clay× 1.43× 0.9× 0.7× 1.59
    Rock (blasted)× 1.5× 1.3× 0.67× 1.15
    Coral (comparable to limerock)× 1.5× 1.3× 0.67× 1.15

    FM 5-434, Table 1-1. Note the rock row: blasted rock compacts to 1.30 of its bank volume, because you cannot put broken rock back the way it was.

    Sloping the sides

    A hole with vertical walls is a drawing. A hole you can stand in has battered sides, and that makes it a truncated pyramid rather than a box — worked here with the prismoidal formula rather than by averaging the two ends, because averaging over-states a shape tapering in two directions at once. Battering the same excavation at 1:1 takes it from 29.63 to 50.57 cubic yards.

    What slope your soil actually needs is a safety question governed by OSHA's soil classification and by what is on your site. This calculator will work out the volume for any batter you give it and will not suggest one, because a trench that collapses does not do it slowly.

    What this does not tell you

    • Whether it is safe to dig. Shoring, benching and sloping requirements come from OSHA and from a competent person on site.
    • What is buried down there. Call before you dig. Services, not soil, are what turn an excavation into an incident.
    • Rock and water. Both change the price by more than the volume does, and neither shows up in a length times width.
    • What it costs. The volume is ours and it is cited; the rate per yard is yours and it is regional.

    The rest of the job

    What goes back in is usually not what came out. The topsoil calculator works out imported soil for the same footprint, gravel covers granular backfill and base, and for a trench that has to drain, the french drain calculator handles the stone around the pipe. If the hole is for a footing or a post, the post depth calculator and the post hole calculator size it, and the concrete weight calculator handles the other heavy thing on the same trailer.

    Section through a 20 foot wide excavation dug 4 feet deep, the hole a bank volume is measured in.
    Drawn to scale.

    Common questions

    How do you calculate excavation volume?

    Length times width times depth gives the hole, and then you have to convert it, because soil does not stay the size of the hole it came out of. A 20 by 10 by 4 foot excavation is 29.63 cubic yards in the ground — the bank volume — and 34.07 to 40 cubic yards once it is dug and piled. Everything you pay for after the digging is billed on the second figure.

    What is a swell factor?

    How much bigger soil gets when you disturb it, expressed as a percentage increase in volume. Digging creates voids that were not there when the ground was compacted by its own weight. US Army FM 5-434 puts dry sand and gravel at 10 to 15 percent, dry earth at 15 to 35, dry clay at 40 and shale at 65 — so the same hole produces very different piles depending on what is in it. Multiply bank volume by one plus the swell to get loose volume.

    What is the difference between bank, loose and compacted cubic yards?

    Bank is the material sitting undisturbed in the ground — the size of the hole. Loose is the same material after it has been dug, which is bigger. Compacted is the same material placed and rolled into a fill, which is usually smaller than bank. They are three measurements of one pile of dirt, and confusing them is the classic earthworks error: a supplier quotes loose yards, a drawing specifies compacted yards, and neither says so.

    How many truck loads will my excavation be?

    Divide the LOOSE volume by the truck capacity, never the bank volume. On the example above, 29.63 bank yards in a 10 yard truck looks like 3 loads and is actually 4. That is a whole extra trip on a hole barely bigger than a garage, and it is the single most common way an excavation budget goes over.

    Do I need to allow for sloping the sides?

    Almost always, and it is a big number. Trench and pit walls are cut back for stability, and a hole battered at 1:1 is a truncated pyramid rather than a box. The same 20 by 10 by 4 foot excavation with 1:1 sides holds 50.57 cubic yards instead of 29.63 — 71 percent more. What slope your soil needs is an OSHA classification question and a site question, not something this or any calculator can decide.

    How much does excavated soil weigh?

    Between 2,180 and 2,980 pounds a bank cubic yard for dry earth, and more when it is wet — wet earth runs 3,500 to 4,000. The table below gives every published figure. Weight matters more than volume when you are hiring a skip or loading a trailer, because you will usually reach the weight limit first.

    Will the soil fill the hole again if I backfill?

    No, and this surprises people every time. Soil swells when dug and then compacts to less than its bank volume when it is properly placed and rolled — dry clay comes back to about 90 percent of what it was. So a trench backfilled with its own spoil leaves a surplus at first and a depression a season later once the fill settles. Plan for both: somewhere to put the excess, and material to top up.

    Where do these figures come from?

    US Army Field Manual FM 5-434, Earthmoving Operations, Tables 1-1 and 1-2. It is a public-domain document, it names the materials it is talking about, and it publishes bands rather than single numbers. Nothing on this page is a swell factor anybody here made up, and where the manual gives a range this calculator gives you the range rather than picking an end of it.

    Sources

    Two published tables from one public-domain source, kept separate because the manual keeps them separate. Table 1-2 carries swell, load factor and weight for eleven named materials and is what the calculator works from. Table 1-1 carries the full six-way conversion between bank, loose and compacted for five broader material classes, and is published on the page as a reference rather than read by the calculator. Merging them would mean picking a Table 1-2 row to stand for a Table 1-1 class, which is a choice nobody published. Swell is stored as the band the manual prints, not as a midpoint: dry earth is 15 to 35 percent, and the difference between those ends is two extra truck loads in twenty.

    Unit conversions are exact by definition and need no source.

    How we choose and cite these figures

    By Team MaterialMath. Published . How these figures are sourced and checked.