Perimeter of a Sector Calculator — Arc + Two Radii
Find the perimeter of a circular sector (a "pie slice") in one step — enter the radius and the central angle in degrees or radians to get the arc length, the two-radii contribution, and the total boundary length.
Angle unit
2r + arc = 2 × 5 + 7.854
- 1
Convert angle to radians
90 × π ÷ 180 = 1.570796 - 2
Arc length = r × θ
5 × 1.570796 = 7.854 - 3
Two radii = 2r
2 × 5 = 10 - 4
Perimeter = 2r + arc
10 + 7.854 = 17.8540
How does this calculator work?
The perimeter of a circular sector is P = 2r + rθ = r(2 + θ), where θ is the central angle in radians. It is made up of two radii (2r) and one arc (rθ). Enter the radius and central angle (degrees or radians) to get the perimeter and the arc length separately.
Formula
How this is calculated
A circular sector looks like a "pie slice": it is bounded by two straight radii and one curved arc. The perimeter is the total length of all three boundaries. The two radii each contribute length r, so together they add 2r. The arc length equals rθ, where θ is the central angle measured in radians. Adding both parts gives the sector perimeter: P = 2r + rθ = r(2 + θ).
If the angle is given in degrees, convert first: θ_rad = θ_deg × π / 180. For example, a quarter circle (90°) has θ = π/2, so P = 2r + r·(π/2) = r(2 + π/2) ≈ 3.571r. A semicircle (180°) gives P = 2r + πr = r(2 + π) ≈ 5.142r. A full circle sector (360°) would give P = 2r + 2πr, but that counts the two radii of a closed circle which overlap — in practice a full circle has no radii, just the circumference.
The sector area is also computed as ½r²θ (in radians). These formulas assume a perfect circle and a central angle measured at the circle's centre. They apply to problems such as finding the perimeter of a fan blade, a clock-hand sweep region, or a pizza slice.
Frequently asked questions
P = 2r + rθ, where r is the radius and θ is the central angle in radians. If you have the angle in degrees, multiply by π/180 first to convert. The arc length portion is rθ and the two straight sides together are 2r.
No. The arc length is only the curved part of the boundary: arc = rθ. The full perimeter includes the two straight radii as well: P = 2r + arc. Confusing them gives an answer that is 2r too small.
A semicircle has a central angle of 180° = π radians. Applying the formula: P = 2r + r·π = r(2 + π). For example, a semicircle of radius 5 has perimeter 5 × (2 + π) ≈ 25.71.
Also known as
TG we-Calculate Editorial Team. (2026). Perimeter of a Sector Calculator — Arc + Two Radii [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/perimeter-of-a-sector-calculator
TG we-Calculate Editorial Team. "Perimeter of a Sector Calculator — Arc + Two Radii." TG we-Calculate. 2026. https://we-calculate.com/calculator/perimeter-of-a-sector-calculator.
TG we-Calculate Editorial Team, "Perimeter of a Sector Calculator — Arc + Two Radii," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/perimeter-of-a-sector-calculator
@misc{wecalculate_perimeter_of_a_sector_calculator, title = {Perimeter of a Sector Calculator — Arc + Two Radii}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/perimeter-of-a-sector-calculator}}, year = {2026}, note = {TG we-Calculate} }
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