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Sector arc length & area solver with diagram

Find arc length l, area A, central angle θ, or radius r in one tool. See the θ/360 ratio, units (cm/cm²/°), and a live sector diagram with step-by-step explanations.

A starter example (r=6cm, θ=120°) is preloaded so the result and diagram appear immediately. Calculations stay in your browser unless you copy a link.

Other languages: English | 日本語 | Español

How to use (3 steps)

  1. Pick Explore to move r and θ freely, or Solve to lock one unknown and enter the other two.
  2. Fill two known values with their units visible. Example chips set clean values instantly.
  3. Read the result, θ/360 ratio, diagram, validation vs 2πr and πr², and the step cards. Copy a URL, LaTeX, or the SVG if needed.

Teacher mode enlarges text, keeps the ratio visible, and is friendly to projectors and low-motion settings.

Unknown (Solve mode)

In solve mode, leave the unknown blank and enter the other two values (or tap an example chip).

cm
°
cm
cm²
Display & accessibility

FAQ

How do I find the arc length of a sector?

Multiply the full circumference 2πr by the portion p = θ ÷ 360. The tool shows l = p × 2πr and checks the result against the circle.

Why do we multiply by θ ÷ 360?

A sector is the same fraction of the circle as its angle. The same proportion shrinks both the circumference and the area.

Which units can I use?

Select mm, cm, m, or km. The area unit follows automatically (for example cm²). Angles default to degrees; switch to radians if you prefer.

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