Computational Design Calculator

Computational Design Calculator

Calculator Overview

This skill provides 7 production-grade Python calculators purpose-built for computational design workflows in Architecture, Engineering, and Construction (AEC). Each calculator is a standalone command-line tool that accepts domain-specific parameters and returns precise, well-formatted results.

All calculators share common design principles:

• Human-readable output by default with clear section headers, formatted tables, and summary statistics.
• --json flag on every calculator for structured machine-readable output, enabling pipeline integration with parametric design tools, Grasshopper scripts, Dynamo graphs, or custom automation.
• Strict input validation with meaningful error messages that guide the user toward correct usage.
• SI units throughout (millimeters for geometry, kilonewtons for forces, degrees for angles) with Imperial equivalents noted where relevant.
• Deterministic calculations based on published engineering formulas (Eurocode, ASCE, ASHRAE) so results can be cross-checked and audited.

Calculator Index

#	Calculator	Script	Primary Domain
1	Geometry Calculator	geometry_calculator.py	Cross-section properties
2	Structural Checker	structural_checker.py	Member sizing & verification
3	Solar Calculator	solar_calculator.py	Solar position & radiation
4	Panel Optimizer	panel_optimizer.py	Facade rationalization
5	Mesh Analyzer	mesh_analyzer.py	Mesh quality & topology
6	Material Estimator	material_estimator.py	Quantity takeoff & carbon
7	Fabrication Calculator	fabrication_calculator.py	CNC / 3D print / laser costing

Directory Structure

cd-calculator/
  SKILL.md                          # This file
  references/
    formulas.md                     # Complete formula reference
  scripts/
    geometry_calculator.py          # Cross-section geometry
    structural_checker.py           # Beam/column/deflection checks
    solar_calculator.py             # Solar position & radiation
    panel_optimizer.py              # Panel clustering & waste
    mesh_analyzer.py                # OBJ mesh quality analysis
    material_estimator.py           # Material quantity takeoff
    fabrication_calculator.py       # Fabrication time & cost

---

1. Geometry Calculator

Script: scripts/geometry_calculator.py

Computes cross-section properties for common AEC shapes used in structural analysis, fabrication planning, and parametric design. All inputs are in millimeters; all outputs are in mm-based units (mm^2, mm^4, etc.).

Supported Shapes

Shape	Description	Key Parameters
rectangle	Solid rectangular section	width, height
circle	Solid circular section	radius
triangle	Solid triangular section	base, height
i-beam	Standard I/H section	width, height, flange thickness, web thickness
hollow-rect	Rectangular hollow section (RHS)	width, height, wall thickness
hollow-circle	Circular hollow section (CHS)	outer radius, inner radius
l-shape	L-angle section	width, height, thickness
t-shape	T-section	width, height, flange thickness, web thickness
polygon	Arbitrary polygon	vertex coordinates

Parameters

Parameter	Type	Unit	Description
--shape	string	--	Shape type (required)
--width	float	mm	Overall width
--height	float	mm	Overall height
--radius	float	mm	Radius for circular sections
--outer-radius	float	mm	Outer radius for hollow circle
--inner-radius	float	mm	Inner radius for hollow circle
--base	float	mm	Base width for triangle
--flange-thickness	float	mm	Flange thickness for I-beam / T-shape
--web-thickness	float	mm	Web thickness for I-beam / T-shape
--wall-thickness	float	mm	Wall thickness for hollow sections
--thickness	float	mm	Leg thickness for L-shape
--vertices	string	mm	Comma-separated x,y pairs for polygon
--json	flag	--	Output as JSON

Example Usage

# Solid rectangle 300 x 500 mm
python geometry_calculator.py --shape rectangle --width 300 --height 500

# Circular section with 150 mm radius
python geometry_calculator.py --shape circle --radius 150

# Standard I-beam
python geometry_calculator.py --shape i-beam --width 200 --height 400 --flange-thickness 15 --web-thickness 10

# Hollow rectangular section
python geometry_calculator.py --shape hollow-rect --width 300 --height 300 --wall-thickness 12

# JSON output for pipeline integration
python geometry_calculator.py --shape rectangle --width 300 --height 500 --json

Sample Output

========================================
  GEOMETRY CALCULATOR - Rectangle
========================================

  Dimensions:
    Width  (b) :   300.00 mm
    Height (h) :   500.00 mm

  Section Properties:
    Area             :   150,000.00 mm²
    Perimeter        :     1,600.00 mm
    Centroid (x, y)  :   (150.00, 250.00) mm

  Second Moment of Area:
    Ix (about x-axis):   3,125,000,000.00 mm⁴
    Iy (about y-axis):   1,125,000,000.00 mm⁴

  Section Modulus:
    Sx               :    12,500,000.00 mm³
    Sy               :     7,500,000.00 mm³

  Radius of Gyration:
    rx               :       144.34 mm
    ry               :        86.60 mm
========================================

---

2. Structural Checker

Script: scripts/structural_checker.py

Performs quick structural sizing and verification checks for steel members based on simplified Eurocode 3 and ASCE 7 formulas. Designed for early-stage feasibility assessments, not detailed design.

Check Types

Check	Description	Key Inputs
beam	Bending capacity and section sizing	span, UDL, steel grade
column	Axial capacity and buckling check	axial load, height, steel grade
deflection	Serviceability deflection check	span, UDL, section properties

Parameters

Parameter	Type	Unit	Description
--check	string	--	Check type: beam, column, deflection
--span	float	mm	Beam span or effective length
--load	float	kN/m or kN	UDL for beams, axial for columns
--steel-grade	string	--	S235, S275, S355
--height	float	mm	Column height
--buckling-length-factor	float	--	Effective length factor (default 1.0)
--moment-of-inertia	float	mm^4	Section Ix for deflection check
--section	string	--	Named section (e.g., IPE300)
--deflection-limit	string	--	L/250, L/360, or custom (default L/250)
--json	flag	--	Output as JSON

Example Usage

# Size a beam: 6m span, 15 kN/m UDL, S355 steel
python structural_checker.py --check beam --span 6000 --load 15 --steel-grade S355

# Check a column: 2000 kN axial, 4m height, S355
python structural_checker.py --check column --load 2000 --height 4000 --steel-grade S355

# Deflection check with named section
python structural_checker.py --check deflection --span 8000 --load 10 --section IPE300

Sample Output

========================================
  STRUCTURAL CHECKER - Beam Sizing
========================================

  Input:
    Span             :  6,000 mm (6.00 m)
    UDL              :  15.00 kN/m
    Steel Grade      :  S355 (fy = 355 MPa)

  Bending Analysis:
    Max Moment (M)   :  67.50 kN·m
    Required Sx      :  190,141 mm³
    Suggested Section:  IPE 270 (Sx = 429,000 mm³)

  Shear Analysis:
    Max Shear (V)    :  45.00 kN
    Shear Utilization:  0.12  [OK]

  Deflection:
    Max Deflection   :  10.82 mm
    Limit (L/250)    :  24.00 mm
    Utilization      :  0.45  [OK]

  Overall Status:    PASS
========================================

---

3. Solar Calculator

Script: scripts/solar_calculator.py

Computes solar geometry, shadow projections, and photovoltaic parameters for any location on Earth at any date and time. Essential for daylighting analysis, shadow studies, and PV system sizing in early-stage design.

Parameters

Parameter	Type	Unit	Description
--latitude	float	deg	Site latitude (-90 to 90)
--longitude	float	deg	Site longitude (-180 to 180)
--date	string	--	Date in YYYY-MM-DD format
--time	string	--	Solar time in HH:MM format
--annual-summary	flag	--	Monthly solar data summary
--shadow-analysis	flag	--	Shadow length computation
--object-height	float	m	Object height for shadow analysis
--pv-tilt	flag	--	Optimal PV tilt calculation
--json	flag	--	Output as JSON

Example Usage

# Solar position for London at noon on summer solstice
python solar_calculator.py --latitude 51.5 --longitude -0.12 --date 2025-06-21 --time 12:00

# Annual summary for Dubai
python solar_calculator.py --latitude 25.2 --longitude 55.3 --annual-summary

# Shadow analysis for a 30m building in New York
python solar_calculator.py --latitude 40.7 --longitude -74.0 --shadow-analysis --object-height 30

# Optimal PV tilt for Berlin
python solar_calculator.py --latitude 52.5 --longitude 13.4 --pv-tilt

Sample Output

========================================
  SOLAR CALCULATOR - Position
========================================

  Location:
    Latitude         :   51.500° N
    Longitude        :   -0.120° W
    Date             :   2025-06-21

  Solar Position at 12:00:
    Altitude         :   62.07°
    Azimuth          :  180.00° (South)

  Day Information:
    Sunrise          :   03:43 solar time
    Sunset           :   20:21 solar time
    Day Length       :   16h 38m

  Shadow (per 1m object):
    Shadow Length    :    0.53 m
    Shadow Direction :    0.00° (North)
========================================

---

4. Panel Optimizer

Script: scripts/panel_optimizer.py

Rationalizes facade panel inventories by clustering similar panel dimensions within a configurable tolerance, then estimates material waste and cost impacts. Critical for design-for-manufacture workflows in curtain wall and cladding systems.

Parameters

Parameter	Type	Unit	Description
--panels	string	mm	Comma-separated WxH panel dimensions
--tolerance	float	mm	Grouping tolerance (default 10)
--sheet-width	float	mm	Raw sheet/stock width
--sheet-height	float	mm	Raw sheet/stock height
--cost-per-unique	float	$	Cost premium per unique type (default 500)
--json	flag	--	Output as JSON

Example Usage

# Basic panel clustering
python panel_optimizer.py --panels "1200x800,1200x810,1205x800,1200x800,1190x795,1200x800,2400x800,2400x810"

# With sheet size for waste estimation
python panel_optimizer.py --panels "1200x800,1200x810,1205x800" --tolerance 15 --sheet-width 3000 --sheet-height 2000

# Cost-focused analysis
python panel_optimizer.py --panels "1200x800,1200x810,1205x800,1500x900,1510x895" --cost-per-unique 750

Sample Output

========================================
  PANEL OPTIMIZER - Clustering
========================================

  Input Summary:
    Total Panels     :   8
    Raw Unique Sizes :   5
    Tolerance        :  10 mm

  Panel Families:
    Family 1 (1200 x 800 mm):
      Members: 1200x800, 1200x810, 1205x800, 1190x795, 1200x800, 1200x800
      Count: 6
    Family 2 (2400 x 800 mm):
      Members: 2400x800, 2400x810
      Count: 2

  Rationalization:
    Unique types (before) :   5
    Unique types (after)  :   2
    Reduction             :  60.0%

  Cost Impact:
    Uniqueness premium    :  $1,000.00
    Savings vs. raw       :  $1,500.00
========================================

---

5. Mesh Analyzer

Script: scripts/mesh_analyzer.py

Evaluates mesh quality and topological properties for architectural meshes. Reads standard OBJ files or accepts inline vertex/face data. Essential for assessing mesh suitability for FEA, fabrication unfolding, and rendering.

Parameters

Parameter	Type	Unit	Description
--file	string	--	Path to OBJ file
--vertices	string	--	Inline vertices: "x,y,z;x,y,z;..."
--faces	string	--	Inline faces: "i,j,k;i,j,k;..."
--json	flag	--	Output as JSON

Example Usage

# Analyze an OBJ file
python mesh_analyzer.py --file model.obj

# Analyze inline mesh data (a simple quad split into two triangles)
python mesh_analyzer.py --vertices "0,0,0;1,0,0;1,1,0;0,1,0" --faces "0,1,2;0,2,3"

# JSON output
python mesh_analyzer.py --file facade_mesh.obj --json

Sample Output

========================================
  MESH ANALYZER
========================================

  Topology:
    Vertices         :       4
    Faces            :       2
    Edges            :       5
    Euler Char. (V-E+F):    1
    Genus            :       0
    Is Manifold      :     Yes
    Boundary Edges   :       4

  Face Area Statistics:
    Min Area         :   0.500 units²
    Max Area         :   0.500 units²
    Mean Area        :   0.500 units²
    Std Dev          :   0.000 units²
    Total Area       :   1.000 units²

  Aspect Ratio Statistics:
    Min              :   1.000
    Max              :   1.414
    Mean             :   1.207
    Faces > 3.0      :       0  (0.0%)

  Normal Consistency  :   PASS (all normals consistent)

  Bounding Box:
    X range          :   0.000 to 1.000 (1.000)
    Y range          :   0.000 to 1.000 (1.000)
    Z range          :   0.000 to 0.000 (0.000)
========================================

---

6. Material Estimator

Script: scripts/material_estimator.py

Estimates material quantities, weights, and embodied carbon for buildings at the early design stage. Operates in two modes: parametric (from building type and GFA) or direct (from explicit material quantities).

Parameters

Parameter	Type	Unit	Description
--building-type	string	--	residential, office, industrial, retail
--gfa	float	m^2	Gross floor area
--floors	int	--	Number of floors
--concrete-volume	float	m^3	Direct concrete volume
--steel-ratio	float	kg/m^3	Reinforcement ratio
--glass-area	float	m^2	Direct glass area
--timber-volume	float	m^3	Direct timber volume
--waste-factor	float	--	Override waste factor (e.g. 1.10)
--include-embodied-carbon	flag	--	Calculate embodied carbon
--json	flag	--	Output as JSON

Example Usage

# Parametric estimate for a residential building
python material_estimator.py --building-type residential --gfa 5000 --floors 8

# Direct material quantities with embodied carbon
python material_estimator.py --concrete-volume 450 --steel-ratio 120 --glass-area 2000 --include-embodied-carbon

# Office building with custom waste factor
python material_estimator.py --building-type office --gfa 12000 --floors 20 --waste-factor 1.12 --include-embodied-carbon

Sample Output

========================================
  MATERIAL ESTIMATOR - Parametric
========================================

  Building Parameters:
    Type             :  Residential
    Gross Floor Area :  5,000.00 m²
    Floors           :       8
    Floor Area/Floor :    625.00 m²

  Material Quantities (incl. waste):
    Concrete         :    750.00 m³  (1,800.00 tonnes)
    Rebar Steel      :     67.50 tonnes
    Structural Steel :     50.00 tonnes
    Glass            :    500.00 m²  (6.25 tonnes)
    Timber           :     75.00 m³  (33.75 tonnes)

  Total Weight       :  1,957.50 tonnes

  Embodied Carbon:
    Concrete         :  187,500 kgCO2e
    Rebar Steel      :  101,250 kgCO2e
    Structural Steel :   75,000 kgCO2e
    Glass            :    6,875 kgCO2e
    Timber           :  -10,125 kgCO2e (carbon stored)
    ─────────────────────────────────
    Total            :  360,500 kgCO2e
    Per m² GFA       :    72.10 kgCO2e/m²
========================================

---

7. Fabrication Calculator

Script: scripts/fabrication_calculator.py

Estimates fabrication time and cost for three digital fabrication processes: CNC milling, FDM 3D printing, and laser cutting. Uses industry-standard feed rates, material costs, and process parameters.

Parameters

Parameter	Type	Unit	Description
--process	string	--	cnc-milling, 3d-print, laser-cut
--path-length	float	mm	CNC tool path length
--tool-changes	int	--	Number of CNC tool changes
--material	string	--	Material type (varies by process)
--feed-rate	float	mm/min	Override default feed rate
--volume	float	cm^3	3D print volume
--height	float	mm	3D print height
--layer-height	float	mm	3D print layer height
--infill	float	%	3D print infill (default 20)
--cut-length	float	mm	Laser cut total path length
--thickness	float	mm	Material thickness for laser
--hourly-rate	float	$/hr	Machine/labor rate (default 75)
--json	flag	--	Output as JSON

Example Usage

# CNC milling job in wood
python fabrication_calculator.py --process cnc-milling --path-length 5000 --tool-changes 3 --material wood

# 3D print estimate
python fabrication_calculator.py --process 3d-print --volume 500 --height 200 --layer-height 0.2

# Laser cutting acrylic
python fabrication_calculator.py --process laser-cut --cut-length 8000 --material acrylic --thickness 6

# Custom hourly rate
python fabrication_calculator.py --process cnc-milling --path-length 12000 --tool-changes 5 --material aluminum --hourly-rate 120

Sample Output

========================================
  FABRICATION CALCULATOR - CNC Milling
========================================

  Process Parameters:
    Material         :  Wood (Hardwood)
    Path Length       :  5,000.00 mm
    Feed Rate        :  3,000 mm/min
    Tool Changes     :       3
    Change Time      :    2.00 min each

  Time Estimate:
    Cutting Time     :    1.67 min
    Tool Change Time :    6.00 min
    Setup Time       :   15.00 min
    Total Time       :   22.67 min (0.38 hr)

  Cost Estimate:
    Machine Time     :   $28.33
    Material (est.)  :   $15.00
    ─────────────────────────────
    Total            :   $43.33

========================================

---

Usage Notes

Integration with Parametric Tools

All calculators support --json output for integration with parametric design pipelines:

import subprocess, json

result = subprocess.run(
    ["python", "geometry_calculator.py", "--shape", "rectangle",
     "--width", "300", "--height", "500", "--json"],
    capture_output=True, text=True
)
data = json.loads(result.stdout)
area = data["area"]

Chaining Calculators

Calculators can be chained for multi-step workflows. For example, compute section properties, then verify structural adequacy:

# Step 1: Get section properties
python geometry_calculator.py --shape i-beam --width 200 --height 400 \
  --flange-thickness 15 --web-thickness 10 --json > section.json

# Step 2: Check deflection with computed Ix
python structural_checker.py --check deflection --span 8000 --load 10 \
  --moment-of-inertia 198540000

Error Handling

All calculators validate inputs and return meaningful error messages:

ERROR: --radius must be a positive number.
ERROR: --shape 'hexagon' is not supported. Choose from: rectangle, circle, triangle,
       i-beam, hollow-rect, hollow-circle, l-shape, t-shape, polygon.
ERROR: --inner-radius (160 mm) must be less than --outer-radius (150 mm).

Exit codes: 0 for success, 1 for input errors, 2 for computation errors.

Units Convention

Quantity	Unit	Notes
Length / dimensions	mm	All geometry inputs
Area	mm^2	Cross-section areas
Volume (geometry)	mm^3	Section volumes per unit length
Moment of inertia	mm^4	Second moment of area
Section modulus	mm^3	Elastic section modulus
Force	kN	Structural loads
Stress	MPa (N/mm^2)	Steel yield, concrete fck
Moment	kN*m	Bending moments
Angle	degrees	Solar angles, bearings
Building area	m^2	GFA, floor areas
Material volume	m^3	Concrete, timber
Mass	tonnes (1000 kg)	Material weights
Carbon	kgCO2e	Embodied carbon
Fabrication length	mm	Tool paths, cut lengths
Cost	$ (currency units)	Fabrication costs
Time	minutes	Fabrication time

---

Formula Reference

For the complete mathematical formulas behind every calculation, see references/formulas.md. This includes derivations, source standards, and unit conversion tables.

---

Version History

Version	Date	Changes
1.0.0	2026-03-23	Initial release with 7 calculators