CMHA & ASTM Planning Framework

Precision Calculation Methodology

PaverPlan was created to replace inaccurate online calculators with verifiable planning formulas based on North American hardscape industry standards.

Execution Architecture

How PaverPlan Calculates Project Requirements

User Measurements

Exact dimensions, geometry, units, and site-specific allowance.

Published Guidance

ASTM C936, ASTM C33, and CMHA technical specifications.

Derived Formulas

Planning order allowances, void ratios, and modular spacing math.

Planning Output

Net raw, planned volume, and commercial packaging units.

Pillar 1

Strict Material Separation

Generic calculators often conflate bedding sand with joint stabilization sand. At PaverPlan, bedding sand is modeled as a nominal 1-inch uncompacted layer using sand meeting applicable ASTM C33 material requirements. Joint sand is modeled independently based on paver aspect ratio and joint void volume.

Pillar 2

Face Area vs. Installed Modular Pitch

The nominal face area of a paver (L × W) differs from its installed footprint ((L + joint) × (W + joint)). Our engine allows users to explicitly toggle between face coverage and modular pitch, preventing cumulative measurement drift.

Pillar 3

Base Aggregate Footprint & Planning Allowance

Stable subbase preparation requires sound compaction and edge restraint seating. Our engine supports user-selected planning allowances and configurable perimeter base overhang so mechanical edge spikes anchor into compacted aggregate rather than uncompacted soil.

Pillar 4

Full Audit Trail Transparency

Every calculation provides an auditable step-by-step breakdown displaying raw mathematical equations, unit conversion steps, waste additions, and commercial purchase rounding increments. No black-box approximations.

Mathematical Documentation

Representative Core Formulas

MATHEMATICAL FORMULAPaver Unit Quantity Formula

Quantity = ceil( (Total Area / Unit Area) × (1 + Waste Factor) )

Nominal Face Area = (Length × Width) ÷ 144. When tight joint pitches are factored, Installed Modular Area = ((Length + Joint) × (Width + Joint)) ÷ 144.

Variable Legend

Total Area:: Calculated surface area of the project footprint (sq ft)
Unit Area:: Nominal face area (L × W) or installed modular area ((L + Joint) × (W + Joint)) (sq ft)
Waste Factor:: Allowance for edge cuts, diagonal trimming, and handling breakage (typically 5%–15%) (decimal)

MATHEMATICAL FORMULACompacted Aggregate Volume & Tonnage Formula

V_compacted = (A_base × Depth / 12) ÷ 27 | V_order = V_compacted × (1 + Allowance) | Weight = V_order × Density

Base material extends horizontally beyond unconfined paver edges (typically equal to base depth or per restraint manufacturer recommendations) so anchoring spikes drive directly into compacted stone rather than uncompacted topsoil.

Variable Legend

A_base:: Base footprint area: project area plus configurable base extension beyond edge restraints (sq ft)
Depth:: User-selected compacted layer design thickness (planning presets: 4", 6", 8", 10", 12", custom) (inches)
Allowance:: Loose-order allowance for compaction shrinkage and grade variance (planning presets: 0%, 5%, 10%, 15%, 20%, custom) (decimal)
Density:: Planning bulk loose density of crushed stone aggregate (optional user/supplier density, reference baseline: 1.40 tons/cu yd or 103.7 lbs/cu ft) (tons / cu yd)

MATHEMATICAL FORMULANominal Bedding Sand Volume & Order Formula

V_screed = (Area × Depth / 12) ÷ 27 | V_order = V_screed × (1 + Allowance) | Weight = V_order × Density | Bags = ceil( Weight / BagWeight )

Bedding sand is screeded in a loose condition; it is NOT pre-compacted prior to laying pavers. Initial compaction occurs from the top of pavers after placement. Bedding sand area equals the paver surface footprint and does not automatically expand by the aggregate base extension.

Variable Legend

Area:: Project surface area receiving pavers and bedding sand (sq ft)
Depth:: Nominal uncompacted screed depth (CMHA nominal conventional screed depth: 1.0", project-specific presets: 0.75", 1.0", 1.25", custom) (inches)
Allowance:: Ordering allowance for rail tracks, minor base grade variations, and loose handling (typically 5%) (decimal)
Density:: Planning bulk density of washed concrete sand (optional user/supplier density, reference baseline: 1.35 tons/cu yd or ~100 lbs/cu ft) (tons / cu yd)
BagWeight:: Commercial bag unit weight (user-selected options: 40 lb, 50 lb, 60 lb, custom) (lbs)

MATHEMATICAL FORMULADual-Mode Polymeric Joint Sand Estimation Equations

Mode A: Bags = ceil( (Area / Coverage) × (1 + Allowance) ) | Mode B: f_joint = [(L+J)(W+J) - LW] / [(L+J)(W+J)], Joint Vol = Area × f_joint × Depth

Mode A performs direct packaging division based on manufacturer technical data sheet coverage ratings. Mode B models the installed repeating rectangular module ((L+J)(W+J)) to derive the joint area fraction without double-counting shared borders, then optionally converts joint volume to weight using user/product bulk density when supplied.

Variable Legend

Coverage:: Manufacturer published coverage rate per bag for specific paver dimensions and joint geometry (sq ft / bag)
L, W:: Paver unit face length and width (inches)
J:: Installed joint gap width (user/project/product input) (inches)
Depth:: Actual joint fill depth receiving polymeric sand (user/product input) (inches)
Allowance:: Optional user-selected ordering allowance for application buffer, settling, and spillage (decimal)