Interactive 3D Dome Calculator

Diameter

Height, mm

Frequency

Apex Stretch

Dome Thickness, mm

Material Density, kg/m³

This online tool builds an interactive 3D dome and returns core geometric results for the selected dome type. Enter outer diameter and height, adjust a tip stretch parameter to alter the top profile, or switch to the geodesic mode and set frequency. Output includes numeric dimensions, plan views, panel profiles and printable panel templates. The tool is intended for concept design and for generating cutting patterns. It is not a substitute for structural analysis or engineering verification.

Table of Contents

Key features

Real time 3D visualization with orbit and zoom
Three dome modes: spherical segment, geodesic and cloister type
Live recalculation while sliders move
Export preview image and printable panel templates
Estimate area, internal volume, total edge length and approximate mass based on shell thickness and material density
Panel layout and basic flat patterns for geodesic mode

How to use

Select dome type: Segment, Geodesic or Cloister
Enter diameter in feet
Enter dome height in feet
Adjust the Tip Stretch slider to change the top profile
If geodesic is selected set the frequency from 0 to 4
Optionally enter shell thickness and material density to estimate mass
Results update automatically as you change parameters
Use Download to save a preview or template images

Tip Stretch displaces vertices along their local vertical position to produce a sharpened peak or a more rounded top. Meridian and parallel lines follow the deformed shell surface so guide lines remain accurate on the final shape.

Display modes explained

Spherical segment

Constructs a smooth part of a sphere
Best for fast area and volume estimates
Meridians and parallels follow the deformed surface and remain visible as reference lines

Geodesic

Surface built from flat triangular panels
Panels are planar and edges are explicit
Frequency sets the number of subdivisions of an icosahedron and controls panel count
Exportable flat patterns for panel cutting are produced

Cloister

Modified shell featuring concentric ring sections and visible vertical seams
Useful for architectural expressions with ringed layers and clear joints
Meridians and parallels lie on the actual outer surface and do not run inside the model

Controls and behavior

Controls

Type selector instantly rebuilds the model
Diameter control is a slider and numeric input in feet
Height control is a slider and numeric input in feet
Frequency is an integer for geodesic mode from 0 to 4
Tip Stretch adjusts the top profile height in feet
Thickness and density fields estimate shell mass

Interaction details

Camera orientation is preserved while parameters change
Line grids and guide curves are computed after deformation so they match the printable shell
High geodesic frequencies dramatically increase panel count and GPU load

Formulas and notation

Symbols used in formulas

D — outer diameter of the dome in meters for the formulas
a — base radius equal to D divided by 2
H — dome height in meters measured from base to apex
R — radius of the generating sphere in meters
Acap — surface area of the dome segment in square meters
Vcap — internal volume of the dome segment in cubic meters

Because many engineers prefer metric formulas the calculator accepts input in feet and converts internally to meters before applying formulas. The symbolic formulas remain:

Radius of generating sphere R = (H² + a²) / (2 · H)
Surface area of segment Acap = 2 · π · R · H
Segment volume Vcap = π · H² · (3 · R − H) / 3
Plan area Aplan = π · a²
Mass estimate m = Acap · t · ρ where t is thickness in meters and ρ is density in kg per cubic meter

Geodesic counts and panel sizing

For a full sphere subdivided at frequency f the counts are:

Frequency f	Triangles F	Edges E	Vertices V
0	20	30	12
1	80	120	42
2	320	480	162
3	1280	1920	642
4	5120	7680	2562

👉 For a dome segment the number of panels is the full sphere count multiplied by the ratio of the segment area to the full sphere area. Use whole numbers when producing cutting lists.

Approximate side length for roughly equilateral triangular panels

Atri ≈ Acap / N where N is the triangle count for the dome part
a_tri ≈ sqrt( 4 · Atri / sqrt(3) )

Examples in US units

Example	Input	Comment
Small backyard dome	Diameter 20 ft, Height 10 ft	Quick concept for small pavilion
Medium geodesic	Diameter 40 ft, Height 18 ft, Frequency 2	Good balance of panel size and curvature
Large shell	Diameter 100 ft, Height 40 ft	Requires engineering review for structure and loads

Unit conversions reference

Metric	US equivalent
1 meter	3.2808 ft
1 mm	0.03937 in
1 m²	10.7639 ft²
1 m³	35.3147 ft³

Practical guidance and production tips

For fabrication export flat patterns and label each panel with a unique ID and edge pairing to avoid confusion during assembly
Include a cutting allowance and seam overlap. Typical seam allowance is 3 to 10 mm depending on assembly method
When frequency is high panels become small and difficult to fabricate economically. Select frequency balancing visual smoothness and manufacturing efficiency
For wood or composite shells check panel orientation to follow grain direction for best mechanical behavior
Use the mass estimate as a first check only. For structural design calculate loads, supports and connection details with a licensed structural engineer

Limitations and disclaimer

This calculator does not perform structural analysis. It does not check wind, snow or live load capacity
Panel counts and edge lengths are approximate. Final production drawings must be prepared with precise CAD nesting and tolerance allowances
High frequency geodesic models demand significant browser and GPU resources and may slow or crash on underpowered devices
Use results for concept design, visualization and template generation only. Commission an engineer for final structural and building code compliance work

Use the Download option to save a preview image of the model and printable templates for panels. Exported images include the numeric summary, plan, elevations and panel sketches for off-line review.