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Sector Calculator

Geometry

Arc length, area, chord and segment from radius and angle

Quick Answer

Sector Calculator: Arc length, area, chord and segment from radius and angle. Arc = rθ · area = ½r²θ.

Enter any one value, the rest auto-solve
Diagram (updates live with input)
90.00°r = 10.00

Step-by-step

弧长 L = rθ = 10.0000 × 1.5708 = 15.7080

面积 A = ½r²θ = ½ × 10.0000² × 1.5708 = 78.5398

周长 P = L + 2r = 15.7080 + 20.0000 = 35.7080

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How to Use

  1. Enter known values: fill sides, radius or angles in the Sector Calculator.
  2. Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
  3. See formula and steps: the result panel shows the formula used and the substitution.
  4. Try another case: change any known value to solve again.

Key Points

  • Sector Calculator is a free online geometry tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Arc length, area, chord and segment from radius and angle.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Circular sector (radius r, angle θ in radians)

Arc = rθ · area = ½r²θ
Chord = 2r·sin(θ/2) · perimeter = arc + 2r
Segment area = ½r²(θ − sin θ)

FAQ

How do I use the Sector Calculator?
Open the page and fill in the input fields — results update automatically. Arc length, area, chord and segment from radius and angle.
Are the results accurate?
Yes. Standard formulas and conversion factors are used and verified.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. Everything runs locally in your browser.

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Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Sector Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/sector

Results provided by this tool are for reference only and do not constitute professional advice.