Introduction
Every number the Spoil Swell Calculator produces comes from a short chain of formulas: bank volume swells to loose volume, loose volume shrinks to compacted volume, and both convert between cubic meters and cubic yards. This guide derives each formula from first principles — what each term means physically, why the arithmetic takes the shape it does, and how the worked numbers check out in both unit systems. For the full estimating workflow around these formulas, see the complete guide.
The Physical Idea Behind the Formulas
Soil is mostly solid particles with air and water filling the gaps (voids) between them. Undisturbed “bank” soil has been compressed over time, so its void ratio is low — typically 25–40% of its volume is voids. Excavation rips the particle structure apart, and the voids open up: the same mass of soil now occupies more volume. That’s swell — a volume change, not a mass change. Compaction reverses the process, squeezing voids back down. Both formulas below simply express a volume ratio as a percentage.
Formula 1: Loose = Bank × (1 + Swell Factor)
The swell factor is defined as the fractional volume increase on excavation:
Swell factor = (Loose − Bank) ÷ Bank
Rearranging for Loose gives the working formula:
Loose = Bank × (1 + Swell factor)
With a 25% swell factor (0.25), 100 bank cubic yards becomes 100 × 1.25 = 125 loose cubic yards. The multiplier (1 + factor) is just shorthand for “the original volume, plus the swelled portion.” Because the factor is soil-specific, the material guide’s typical ranges (topsoil 10–15%, sand/gravel 10–15%, common earth 20–25%, clay 25–35%, rock 40–60%) are the inputs that make this formula meaningful — the arithmetic is trivial; the soil identification is the skill.
Formula 2: Compacted ≈ Loose ÷ (1 + Shrink Factor)
The shrink factor is the fractional volume decrease under compaction:
Shrink factor = (Loose − Compacted) ÷ Loose
Rearranging for Compacted:
Compacted ≈ Loose ÷ (1 + Shrink factor)
Returning the 125 LCY from above with a 25% shrink factor: 125 ÷ 1.25 = 100 compacted cubic yards — back to approximately the original bank volume. Two things to note. First, the “≈”: field compaction depends on moisture content, lift thickness, and equipment (a sheepsfoot roller achieves more than a plate compactor), so this is a planning conversion, not a lab guarantee — compacted soil rarely returns fully to bank density. Second, the formula inverts naturally for ordering: Loose to order = Compacted needed × (1 + Shrink factor), because delivered fill arrives loose and only shrinks after you compact it. A fuller catalogue of these direction errors is in the common mistakes guide.
Formula 3: Unit Conversion — 1 m³ = 1.308 yd³
One yard equals 0.9144 m, so one cubic yard equals 0.9144³ = 0.7645549 m³. Inverting gives 1 m³ = 1.308 yd³ (1 ÷ 0.7645549). The calculator reports both, and the rule is simple: convert the final volume once, at the end, rather than converting inputs mid-chain where a missed factor hides.
Cross-check with the standard example — 100 BCY of common earth at 25% swell:
- Imperial: 100 × 1.25 = 125 LCY.
- Metric: 100 × 0.7645549 = 76.5 m³ bank; 76.5 × 1.25 = 95.6 m³ loose.
- Agreement check: 95.6 ÷ 76.5 = 1.2497 ≈ 1.25, confirming the swell ratio; and 125 LCY × 0.7645549 = 95.57 m³, confirming the conversion. The two systems describe the same pile.
And a cubic yard contains 27 cubic feet (3³), which is the bridge when dimensions arrive in feet: volume in ft³ ÷ 27 = yd³.
Formula 4: Truckloads = Loose ÷ Truck Capacity
Loads = Loose volume ÷ Truck capacity (loose), always rounded up.
The subtlety is units on both sides: truck beds are rated in loose yards because that’s what they carry. Dividing loose yards by a bank-yard capacity (a mistake some rate sheets invite by quoting “12-yard truck” loosely) undercounts loads. For the 125-LCY example with 12-yd³ tri-axles: 125 ÷ 12 = 10.42 → 11 loads. The 0.42 of a load still needs a truck — fractional loads round up, never down. The estimating guide applies this to full takeoffs.
Worked Mini-Example: Ordering Fill
A void needs 50 compacted cubic yards of common earth backfill at 25% shrink. Running Formula 2 in reverse:
Loose to order = 50 × 1.25 = 62.5 LCY (47.8 m³: 62.5 × 0.7645549 = 47.78).
Trucked in 12-yd³ tri-axles: 62.5 ÷ 12 = 5.21 → 6 loads. Order 5 and the grade finishes one load short — the shrink percentage is exactly the shortfall percentage when fill is ordered in compacted yards. Metric check: 50 yd³ = 38.2 m³ compacted; × 1.25 = 47.8 m³ loose ✓.
How the Factors Combine in a Round Trip
Excavate, haul, and backfill, and the two factors chain: Bank × (1 + swell) ÷ (1 + shrink) = Compacted. With matched 25% factors the round trip returns exactly to bank volume — which is why the factors are often quoted as mirror images. In practice they rarely match exactly: excavation method sets the swell (blasting loosens more than careful digging), while compaction effort sets the shrink. Treat matched factors as a planning convenience and confirm both against the actual methods on site.
Related Guides
- Spoil Swell Calculator: Complete Guide — the full method: terms, formulas, and worked example.
- Spoil Swell Calculator: Material Guide — where the swell and shrink factors come from, by soil type.
- Spoil Swell Calculator: Estimating Guide — applying the formulas to real takeoffs.
- Spoil Swell Calculator: Common Mistakes — the errors these formulas are designed to prevent.
- Spoil Swell Calculator: FAQ — quick answers on the math behind swell.
Get Your Number
The whole chain is four steps: identify the soil and its factors, multiply bank by (1 + swell) for haul-off, divide loose by (1 + shrink) for fill, and convert units once at the end. The Spoil Swell Calculator runs all four and the truckload division — check its outputs against the derivations above until the numbers feel like second nature.
Disclaimer: Calculator results are planning estimates based on the values you enter. Swell and shrink factors are soil- and method-dependent planning values; actual results vary with moisture, excavation method, and compaction effort. Verify against site conditions and consult a licensed professional or your local authority for structural or code-related decisions.
