How this calculator works
Arc length is radius times angle in radians. Adding two radii gives the perimeter of a wedge. The reverse modes rearrange these two equations. Angles may exceed 180° for a major sector, but must be less than a full turn.
Formula
L = rθ; P = r(θ+2) = L+2r; r = P/(θ+2) = (P-L)/2; θ = (P-2r)/r.
Worked example
A quarter-circle sector of radius 2 m has arc π m and perimeter 4+π ≈ 7.14159 m. A semicircle sector of radius 3 m has perimeter 6+3π ≈ 15.42478 m.
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Frequently asked questions
Why add two radii?
Walking around the wedge includes the straight trip from the centre to each end of the arc.
What happens at 360°?
The filled disk has only a circular outer boundary. This tool excludes 360° because the two radial edges disappear there.
Can I recover angle from perimeter?
Yes, if radius is also known. The perimeter must exceed twice the radius and describe less than one full turn.