Core formulas
For a rectangular project in US customary units:
area (ft²) = length (ft) × width (ft)
geometric volume (ft³) = area (ft²) × depth (in) ÷ 12
base order volume = geometric volume × (1 + compaction %) × (1 + waste %)
sand order volume = geometric volume × (1 + waste %)
cubic yards = cubic feet ÷ 27
US short tons = cubic yards × density (short tons/yd³)
bags = round up(order ft³ ÷ bag ft³)
Why two allowances?
The compaction allowance is a planning factor applied only to base aggregate to translate a finished compacted layer toward a loose order quantity. The waste allowance covers handling, grade variation and minor loss, and is applied after the compaction factor. Neither percentage is universal; both remain editable.
Do not double-count.
If a supplier quote already converts compacted volume to loose quantity or includes overage, set the corresponding calculator allowance to zero.
Editable planning defaults
| Input | US default | Why editable |
|---|---|---|
| Base density | 1.50 short ton/yd³ | Gradation, moisture and supplier material vary |
| Sand density | 1.35 short ton/yd³ | Product and moisture vary |
| Compaction allowance | 15% | Loose-to-compacted behavior varies |
| Waste allowance | 5% | Layout, handling and site grade vary |
| Bag volume | 0.5 ft³ | Packaging varies by product |
Acceptance test
For a 12 ft × 16 ft patio, 4 in base, 1 in sand, 15% base compaction allowance, 5% waste and 1.50 short ton/yd³ base density:
- Footprint = 192 ft²
- Base geometric volume = 64 ft³
- Base order volume = 64 × 1.15 × 1.05 = 77.28 ft³
- Base cubic yards = 77.28 ÷ 27 ≈ 2.86 yd³
- Base weight = 2.86 × 1.50 ≈ 4.29 short tons
- Sand order volume = 16 × 1.05 = 16.8 ft³ ≈ 0.62 yd³
The automated test suite checks this example, known-area equivalence, metric equivalence, sand-only calculation and invalid zero dimensions.
Unit conversions
- 1 cubic yard = 27 cubic feet
- 1 cubic meter ≈ 35.3147 cubic feet
- 1 square meter ≈ 10.7639 square feet
- 1 inch = 25.4 millimeters
- 1 US short ton = 0.90718474 metric tonne
Technical source policy
Depth guidance comes from current public documents by CMHA and manufacturer references. The calculator does not copy proprietary calculator output or present a manufacturer system as a universal rule.
- CMHA — Proper Concrete Paver Base and Depth (2025)
- CMHA — Interlocking Concrete Pavers on an Aggregate Base (2025)
- CMHA — Construction of Interlocking Concrete Pavements (2022)
- Unilock — preliminary paver base calculator and disclaimer
- QUIKRETE — Patio Paver Sands data sheet
What the calculator does not calculate
It does not design pavement structure, drainage, slopes, edge restraints, geotextiles, reinforcement, subgrade correction, frost protection, permits or code compliance. It does not know the delivered density, package yield, minimum order or price of a local supplier. Those inputs must be confirmed outside the tool.