Sector Perimeter Calculator

Math

Sector Perimeter Calculator — find the perimeter of a circular sector (radius + arc + radius).

Formula

Arc = r × θ (θ in radians); Perimeter = 2r + Arc
  • A sector is a 'pie slice' of a circle with two radii and an arc.
  • Convert angle from degrees to radians: θ_rad = θ_deg × π/180.
  • Arc length: L = r × θ (use radians).
  • Perimeter: P = 2r + L (two radii plus the arc).

Radius 5, Angle 60°

Inputs
  • Radius (units): 5
  • Central Angle (degrees): 60

θ = 60° = π/3 rad; Arc = 5 × π/3 ≈ 5.24; Perimeter = 10 + 5.24 ≈ 15.24.

Frequently asked questions

What's the difference between a sector and a segment?
A sector is a pie slice (two radii + arc). A segment is the area between a chord and arc (chord + arc, no radii).
How do I convert degrees to radians?
Multiply degrees by π/180. Example: 60° = 60 × π/180 = π/3 radians.
Is the perimeter just the arc length?
No, the sector perimeter includes both radii and the arc: P = 2r + arc.
Can I calculate sector area?
Yes, sector area = (1/2) × r² × θ, where θ is in radians.