Sector Perimeter Calculator

The perimeter of a sector is two straight radii plus the curved arc connecting their tips. Three pieces, not two.

In degrees: P = 2r + (θ / 360) × 2πr In radians: P = 2r + r × θ

The radius contributes twice (one straight side for each radius), and the arc length is the curved part along the outer edge.

Worked example: a quarter-circle garden bed A flower bed in the corner of a yard, 8 ft radius, 90° angle. Two radii: 2 × 8 = 16 ft. Arc: (90/360) × 2π × 8 = 0.25 × 50.27 ≈ 12.57 ft. Total perimeter: 28.57 ft of edging, which is what you would order in metal landscape edging or paver border.

Where sector perimeter matters in practice:

• Garden bed edging. That quarter-circle bed needs 28-29 linear ft of edging. Buy 32 ft (10% buffer for cut waste).
• Fan-shaped patios. A pie-slice patio extending from a circular outdoor kitchen needs trim around the curved edge plus the two straight sides.
• Curved deck or pergola railings. A 120° sector pergola roof with a 10 ft radius needs 2 × 10 + (120/360) × 2π × 10 = 20 + 20.94 ≈ 40.94 ft of fascia trim.
• Cone and funnel blanks. Unrolled, a cone is a sector, so the two straight edges are the seam and the arc becomes the rim.

Quick mental check: what is the arc?

The arc is the fraction of a full circumference, weighted by the angle. A 90° arc is 1/4 of the full circumference; a 60° arc is 1/6. Pizza-cutter math.

Sector perimeter vs. sector area: different quantities, same inputs

Both use r and θ. Perimeter scales with r (linearly), area scales with r² (quadratically). Double the radius of a quarter-pie-slice garden bed and you double the edging length, but quadruple the planting space. Useful trade-off to know when sizing.

Edge case to watch. Enter θ = 360° and the formula returns 2r + 2πr, but a full sector is simply a circle with a stray double-radius line drawn inside it. The real perimeter of a full circle is 2πr. Anything at or near 360° is usually a data-entry slip.