Soil compaction, shrinkage and swell
Two different factors for the same soil, and a published record that disagrees with itself by tens of points. What the tables actually say, and why the number has to be yours.
Last updated 30 September 2026Try your factorTry your numbers
Choose which state you start from (bank, loose or compacted) and enter your own swell or shrinkage. The working shows each step, so you can see which volume is being converted into which.
Loose volume
cubic yards
Waiting on you
Enter your swell for the loose volume, your shrinkage for the compacted volume, or both. The tool has no factor of its own: the published tables differ from one another, and the two that carry a variation note put ±33% on their factors.
Show the calculationHide the calculation2 steps
The working
Loose volume = Bank volume × (1 + Swell)
Compacted volume = Bank volume × (1 − Shrinkage)
Two factors, not one
Loose = Bank × (1 + Swell)
Digging breaks the structure and adds air. Swell depends on the material and how it is dug, and it is the figure hauling is priced on.
Compacted = Bank × (1 − Shrinkage)
Compaction drives air out beyond what the natural ground held. Shrinkage depends on the material, its moisture and — above all — the compaction specified. It is the figure fill is priced on.
Bank needed = Compacted ÷ (1 − Shrinkage); Loose to haul = Bank needed × (1 + Swell)
A fill is specified compacted. To know what to dig or buy you go back to bank; to know what to truck you go on to loose. Both factors, in sequence.
What the published tables actually say
A 2023 research report for the Wisconsin Department of Transportation set out to establish weight–volume relationships for the state’s own soils, and in doing so gathered the published shrink and swell tables into one appendix. Three things stand out in it, and they are the whole argument of this page.
First: the same soil shrinks by a different amount depending on how hard it is compacted. Burch (1997) tabulated the shrink factor — compacted volume as a fraction of bank — for common soils at each compaction specification:
| Material | 95% standard Proctor | 100% standard Proctor | 100% modified Proctor |
|---|---|---|---|
| Dry sand | 0.83 | 0.77 | 0.72 |
| Damp gravel | 0.93 | 0.87 | 0.78 |
| Dry clay | — | 0.94 | 0.82 |
| Dry dirt | — | 0.83 | 0.78 |
Dry sand at 0.72 loses 28% of its bank volume; at 0.83 it loses 17%. Same sand. The specification on the drawing decides which, which is why a table indexed by soil name alone cannot answer the question.
Second: different sources give different figures for the same material. Swell from bank to loose, in percent, as tabulated by the FHWA (2022) and by Church (1981):
| Material | FHWA (2022) | Church (1981) |
|---|---|---|
| Clay, dry | 50% | 35% |
| Earth / loam, dry | 50% | 35% |
| Earth / loam, damp | 43% | 40% |
| Gravel, dry (well graded vs. dry gravel) | 33% | 15% |
| Silt | 36% | 36% |
| Topsoil | 56% | 56% |
Fifteen points apart on dry clay and loam; more than double on gravel. Both are respectable sources. Neither measured your site.
Third: state DOTs set design shrinkage by geography and by job, not by soil. From their manuals as summarised in the same appendix:
| Manual | Condition | Design shrinkage |
|---|---|---|
| TDOT (2021) | Light cuts and fills, 1–2 ft, earth | 30 – 50% |
| TDOT (2021) | Light cuts and fills, 4–6 ft, earth | 15 – 20% |
| TDOT (2021) | Heavy cuts and fills, earth | 10% |
| NCDOT (2021) | Mountains | 15 – 20% |
| NCDOT (2021) | Eastern coastal plain | 25 – 30% |
| InDOT (2013) | Divided roadway, under 1,000 cu yd per 100 ft | 25% |
| InDOT (2013) | Divided roadway, 2,000 cu yd per 100 ft or more | 15% |
Tennessee’s figure for the same earth runs from 10% on a heavy job to as much as 50% on a shallow one, because thin fills lose proportionally more to the subgrade and the edges. North Carolina uses one range in the mountains and another on the coastal plain. These are estimating factors for road design in those states — a useful reference for the order of magnitude, not a value for a site.
And the note the report prints under its table of Church’s factors: swell and shrinkage factors are subject to an average ±33 percent variation, for rock and earth alike. The FHWA exhibit’s own footnote says its factors are subject to ±33% variation. Read as a share of the published figure, which neither note says outright, a published 20% is a published 13-to-27%.
Why a fill shrinks and a cut swells
- Natural ground has a structure with voids in it. Digging destroys the structure and adds air, so the loose volume is larger — swell.
- Compaction squeezes the voids smaller than the natural ground had, so the placed volume is smaller than the bank volume it came from — shrinkage.
- How much smaller depends on the target density in the specification (the Proctor percentage), the moisture at placement, and the equipment. None of those is in the soil’s name.
- Rock is the exception that proves it: blasted rock cannot be compacted back below its bank volume, so its "shrinkage" is a further swell — the tables show it as a positive embankment factor.
Where your factor comes from
- The geotechnical report for the site, which will state shrinkage and swell for the materials it identifies and the compaction it recommends.
- Your state DOT’s design manual, for an estimating range appropriate to the region and the size of the job — the tables above show the kind of thing it will say.
- A test strip: a measured bank volume, placed and compacted to the specification, measured again. This is what the factors in the tables were once, before they became tables.
- Not this page, and not any calculator. This site ships no factor because the sources above show there is no single factor to ship.
The arithmetic, with your figures
Suppose a report gives 15% shrinkage and 25% swell for the material, the drawings call for 100 cubic yards of compacted fill, and the trucks carry 12 loose yards. The two percentages are inputs to the example, not recommendations.
| Step | Working | Result |
|---|---|---|
| Bank volume needed | 100 ÷ (1 − 0.15) | 117.6 cu yd |
| Loose volume to haul | 117.6 × 1.25 | 147.1 cu yd |
| Truck loads | 147.1 ÷ 12, rounded up | 13 |
| Loads if priced on the compacted figure | 100 ÷ 12, rounded up | 9 |
4 extra loads on 100 yards of fill — 44% more trucking than the compacted figure suggests. Change the shrinkage to the other end of the ±33% band and the load count moves again, which is the practical meaning of that caveat.
How Calcumetryx handles it
The swell factor calculator converts between bank, loose and compacted volume from the factors you enter, on either definition of the compaction figure (shrinkage of the bank volume, or expansion of the fill as Wisconsin DOT uses it), and derives a swell and a shrinkage from measured densities. The fill dirt calculator takes the compacted volume and the compaction percentage you enter and reports the loose quantity to order and the truck loads; leave the percentage blank and it says the compacted figure is being used as-is and why that is optimistic. The cut and fill calculator takes swell and shrinkage as two separate optional inputs and reports whether the cut covers the fill in loose terms. None of them carries a default, for the reasons on this page.
- Weight-Volume Relationships and Conversion Factors for Soils and Aggregates of Wisconsin — Final Report, Appendix C: Shrinkage and Expansion (Swell) Factors from Literature Review — Cetin, Bulduk (Michigan State University), Likos, Edil (University of Wisconsin–Madison) for the Wisconsin Department of Transportation, WisDOT ID G22-05, December 2023
- Bank, loose and compacted measure are defined by the formulas above — Arithmetic — verifiable by hand
Put it to work
All earthwork calculators →Enter the factors from your report; each tool shows the working in whichever measure the line item uses.