Sizu Riatto
Every Angle · Chapter 8

Coverage: Sectors and Circles

A camera's view is a slice of a circle. Its area and arc come from the angle; walls and fences cut it back, and a plan drawing shows what is left.

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Opens on the book's house and plot. Change any number to your own and press Calculate.

The camera (plan position in meters: x east from the street-side west corner, y north from the street)

What cuts the view back: the house (a rectangle) and the plot edge

Enter the camera's position, aim and view, then press Calculate.

The formula

  • The range at a DORI level = pixels ÷ (2 × density × tan(view ÷ 2)) (Chapter 6)
  • Sector area = view ÷ 360 × π × range²; arc = view ÷ 360 × 2π × range
  • The ground seen: a ray every half degree, each stopped by a wall or the plot edge; the area of the polygon by the shoelace formula, ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|
  • Cameras to go all the way round, ignoring walls = 360 ÷ the view, rounded up
The book's worked example, Chapter 8. One camera at recognize reaches 8.59 m: a sector of (100/360) π 8.59² = 64.4 m², arc 15.0 m. Cut back by the walls and the plot edge, camera 1 sees 43.5 m², camera 2 26.6, camera 3 62.0, camera 4 62.0, camera 5 12.4. The first plan, four cameras and the doorbell, left the west passage about 90% blind; the fifth camera, aimed 340° along it, closes it.
Check it. Pace the edge of the view on the ground and mark it with canes; film it and check the canes sit at the picture's edges.

Honest limits. The plan counts ground in plain sight from the camera's position; it ignores shrubs, cars, fences inside the plot, night and weather. A sector on paper is where a camera can look, not what it will catch. The book's house was worked out on paper from published figures, not surveyed by us: measure your own, and walk your own plot at night. Prices are illustrative US prices from November 2026, shown without a currency sign; put in your own. Everything stays in your browser: no sign-up, nothing stored.

These calculators go with Every Angle (Make It Add Up, Book 2), where every number on this page is worked by hand.