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Backfill and Compaction Calculator

How many loose cubic yards to order so the hole is full after compaction. Enter the void dimensions (or a known volume), pick the fill material, and see the loose quantity to order plus delivery loads. The calculator accounts for both swell (loose expansion) and shrink (compaction reduction) so you do not come up short.

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The math, shown transparently

No black box. Here is exactly what the calculator computes. The key insight: you need more loose material than the void because loose material compacts down.

// Void volume. The hole you need to fill.

void_ft³ = length × width × depth (imperial)

void_yd³ = void_ft³ / 27

void_m³ = length × width × depth (metric)

void_yd³ = void_m³ / 0.9144³ (NIST yd to m)

// Loose yards to order. Accounts for compaction.

loose_yd³ = void_yd³ × (swell_factor / shrink_factor)

// Delivery loads. Always rounds up.

loads = ceil(loose_yd³ / truck_capacity_yd³)

Worked example

A 10 ft × 10 ft × 10 ft void backfilled with common earth, delivered in a standard 12 yd³ tandem dump:

void_ft³ = 10 × 10 × 10 = 1000 ft³

void_yd³ = 1000 / 27 = 37.04 yd³

swell_factor = 1.25 (common earth)

shrink_factor = 0.90 (10% shrink when compacted)

loose_yd³ = 37.04 × (1.25 / 0.90) = 37.04 × 1.389 = 51.44 yd³

loads = ceil(51.44 / 12) = ceil(4.29) = 5 loads

Compare this to the naive calculation (37.04 / 12 = 4 loads). You would come up short by over a full truckload. The compaction factor matters.

How compaction factors work

Earthwork has three volume states. Understanding all three is essential for ordering the right quantity of backfill material.

  • Bank (in-place): The undisturbed volume in the ground. This is what you measure from plans or survey. It is the baseline, factor 1.0.
  • Loose (excavated/delivered): When material is dug up or dumped from a truck, it occupies more space than bank because air gets between particles. The swell factor converts bank to loose. Common earth swells about 25% (factor 1.25).
  • Compacted (placed and rolled): When material is placed in lifts and compacted with a roller or plate tamper, it shrinks below its loose volume and often below the original bank volume. The shrink factor converts bank to compacted. Common earth shrinks about 10% (factor 0.90, meaning compacted volume is 90% of bank).

The formula loose = void × (swell / shrink) works because you need to fill a void (measured in bank yards) with material that arrives loose and will be compacted. The swell/shrink ratio tells you how much loose material compacts down to fill one bank yard of void.

Special case: blasted rock has a shrink factor greater than 1.0 (factor 1.30). This means even fully compacted, blasted rock never returns to its original bank density. You actually need less loose rock than you might expect because it does not compact as aggressively as soil.

Frequently asked questions

What is the difference between swell and shrink in earthwork?

Swell is the expansion that happens when you dig material out of the ground. Loose dirt takes up more space than in-place bank dirt because air gets in. Shrink is the reduction that happens when you compact material back into a hole. Compacted fill is denser than the original bank state. They are independent measurements, not inverses of each other.

Why do I need more loose material than the hole I am filling?

Loose material has air gaps between particles. When you compact it with a roller or plate, those gaps close and the volume shrinks. If you only order the same volume as the void, you will come up short after compaction. The calculator accounts for both the swell (loose expansion) and the shrink (compaction reduction) to tell you exactly how much to order.

Where do the compaction factors come from?

The swell and shrink factors are sourced from the Caterpillar Performance Handbook earthwork conversion tables and FHWA guidance documents. Shrink values assume Standard Proctor density (95% compaction). Where ranges exist, the mid-range value is used for conservative planning estimates.

Can I use this for gravel base under a slab?

Yes. Select gravel (dry or wet) from the material dropdown. Granular materials like gravel and crushed stone do not compact as much as clay or topsoil, so the loose-to-order multiplier is smaller. The calculator handles it correctly for all material types.

Does the calculator account for subgrade preparation?

No. This calculator tells you how much fill material to order for a given void. It does not account for subgrade preparation, overexcavation, moisture conditioning, or lift thickness requirements. Those are site-specific decisions for your geotechnical engineer or spec.

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