How to use the Cultist Circle Calculator

The Cultist Circle Calculator is a simple interactive tool that computes geometric properties (angular separation, chord length, arc length, circumference, and area) and plots evenly spaced points (cultists) around a circle given the number of participants and the circle’s radius.

How to use the Cultist Circle Calculator (step-by-step)

What this calculator does and why it matters

This calculator helps you place evenly spaced markers—“cultists”—around a circle and instantly see the geometry that results. Whether you’re planning a theatrical blocking, stage prop layout, garden bed layout, ritual prop spacing, or just curious about circle geometry, the tool computes the angular separation between adjacent members and shows both chord and arc distances. It also visualizes the circle using Plotly.js so you can confirm placement visually and interactively.

Quick start: the controls explained

• Number of cultists (N): Enter an integer (≥1). The calculator divides the circle into N equal slices. Set this to the number of people or markers you need.
• Circle radius (units): Provide a radius in any unit (meters, feet, pixels). All distance outputs will use that unit. If you use meters, the area and circumference will reflect meters and square meters.
• Start angle (°): This rotates the arrangement. Useful for orienting the first marker toward a door, camera, or landmark.
• Marker size: Adjust the visual size of plotted points (pixel units for screen clarity).
• Show labels: Toggle whether markers show a small label (e.g., #1, #2) allowing you to reference particular positions.
• Unit label: Optionally type the unit name (e.g., “meters”) to append to results.

Hit Calculate & Draw to run the computation and see the Plotly visualization. Results are shown in a compact table below the plot: angular separation (degrees), chord length (straight line between adjacent markers), arc length (curve along the circle between markers), total circumference, and circle area.

The math the calculator performs (brief)

• Angular separation: 360° / N — the number of degrees between adjacent markers.
• Chord length: 2 * R * sin(π / N) — straight-line distance between two adjacent points.
• Arc length: R * (2π / N) — curved distance along the circumference.
• Circumference: 2πR and Area: πR².

These formulas are computed precisely in the code and presented with numeric rounding for clarity.

How to interpret and use outputs

• Angular separation: Use this to orient performers or props. If the angle is small, objects will be closely packed; if large, they’ll be widely spaced.
• Chord vs Arc length: For physical spacing (clear distance between bodies or props), chord length is the most relevant. If you’re marking positions along the floor line, arc length may be your guide.
• Circumference and area: Useful for material estimates (e.g., tape around the circle) or area coverage inside the circle.

Practical examples

1. Theatre staging: If you need to position 16 cast members evenly around a circular stage with radius 4 meters, set N = 16 and R = 4. Use the start angle to align one actor facing the audience.
2. Garden bed design: For a circular flower bed, the chord length tells you how far apart planting rings will be for uniform visual balance.
3. Photography or drone shots: Use the start angle to orient a subject precisely toward the camera while keeping even spacing between assistants or props.

Design and accessibility notes

• The visual is built with Plotly.js so it’s interactive: hover for coordinates (or labels if enabled), zoom and pan are available on desktop.
• The calculator’s container is intentionally limited to a max-width of 740px and is responsive so it fits between two sidebars in most WordPress themes. It has a white background for clean printing and visual consistency.
• All inputs are easy to modify; there’s a Reset button to return to sensible defaults (12 cultists, radius 3).

Embedding instructions for WordPress

1. Open the post or page editor.
2. Add a Custom HTML block where you want the calculator to appear.
3. Paste the complete HTML/JS block (above) into that Custom HTML block.
4. Update or Preview the page. The calculator will render inline and should fit the content column between sidebars. If your theme has an especially narrow content area, reduce the container max-width in the HTML (e.g., change max-width:740px to max-width:680px).

Tips for best results

• Use integer values for the number of cultists. Non-integers aren’t meaningful for count.
• Match the unit label to what you’re actually using (meters, feet, px) to avoid confusion.
• If physical spacing matters, measure chord length and add a safety margin for movement or props.

Advanced use cases

• Custom orientation: Use the start angle to place a single “leader” at a precise compass direction.
• Large N: The plot will handle many points, but remember visual markers may overlap for very large N; reduce marker size or zoom in.
• Exporting coordinates: Hover over plotted points to see coordinates; these can be transcribed to an external plan or exported by adapting the code to produce a CSV if desired.

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Disclaimer

This calculator provides geometric estimates for evenly spaced points on an ideal mathematical circle. It does not account for human movement dynamics, safety margins, floor irregularities, or building regulations. Always verify physical placement in situ and follow applicable safety guidelines.

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FAQ

Q: Can I use any unit for radius?
A: Yes. Enter the radius in meters, feet, pixels, etc. Add the unit text in the “Unit label” field so results display with context.

Q: What if I need an odd spacing (not evenly spaced)?
A: This tool produces even spacing only. For non-uniform arrangements, you would adjust individual angles and regenerate the plot or modify the code to accept custom angle lists.

Q: Will the plot print well?
A: The background is white and the layout is compact for printing. For higher-quality prints, export a screenshot from the browser’s print dialog or adapt the Plotly export features.

Q: How do I change visual size if my theme’s content column is wider/narrower?
A: Edit the max-width in the wrapper <div> CSS (e.g., set it to 680px or 800px) and update the page.

Q: Can I export coordinates for use in another program?
A: The current version shows coordinates on hover. You can extend the script to generate a CSV or JSON file if needed—ask me and I’ll provide a version that exports coordinates.