Circle Perimeter Calculator — Circumference, Arc & Chord Length
Find the full circumference of a circle and, for any central angle, the arc length, chord length, sector perimeter (arc + two radii), and segment perimeter (arc + chord).
units
°
C = 2π × r — total perimeter of the complete circle
- 1
Angle to radians
90° × π ÷ 180 = 1.570796 - 2
Full circumference
2 × π × 7 = 43.9823C = 2πr — the total distance around the complete circle.
How does this calculator work?
Full circumference C = 2πr. For sector angle θ: arc = (θ/360) × 2πr, chord = 2r·sin(θ/2), sector perimeter = arc + 2r, segment perimeter = arc + chord. Enter radius and angle to get all four values instantly.
Formula
How this is calculated
The perimeter of a complete circle is its circumference C = 2πr. When you cut the circle with two radii at a central angle θ, the curved boundary of that slice is the arc: arc = (θ / 360°) × 2πr. In radians this simplifies to arc = r × θ_rad. The sector (pie-slice shape) has a total perimeter of arc + 2r, since its boundary also includes two straight radius edges.
The chord is the straight line joining the two arc endpoints. Using the law of cosines (or equivalently the inscribed right triangle), chord = 2r × sin(θ/2). The chord is always shorter than the arc. The circular segment (the region between the arc and the chord) has perimeter = arc + chord.
For a semicircle (θ = 180°), the arc is exactly πr ≈ 3.14159 r and the chord equals the diameter 2r. All results scale linearly with r but non-linearly with θ.
Frequently asked questions
A sector is the "pie slice" shape — its perimeter is the arc plus two straight radii (arc + 2r). A segment is the region between a chord and its arc — its perimeter is just the arc plus the chord length, with no radii included.
Arc length = r × θ (radians). For example, a 90° angle is π/2 radians, so arc = r × π/2. The degree formula (θ/360 × 2πr) and the radian formula (r × θ_rad) are equivalent — the calculator accepts degrees.
For θ = 180°: arc = πr, chord (diameter) = 2r, so the total boundary of the semicircular region is πr + 2r ≈ 5.14159 r. For r = 5 this is about 25.71 units.
Also known as
TG we-Calculate Editorial Team. (2026). Circle Perimeter Calculator — Circumference, Arc & Chord Length [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/circle-perimeter-calculator
TG we-Calculate Editorial Team. "Circle Perimeter Calculator — Circumference, Arc & Chord Length." TG we-Calculate. 2026. https://we-calculate.com/calculator/circle-perimeter-calculator.
TG we-Calculate Editorial Team, "Circle Perimeter Calculator — Circumference, Arc & Chord Length," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/circle-perimeter-calculator
@misc{wecalculate_circle_perimeter_calculator, title = {Circle Perimeter Calculator — Circumference, Arc & Chord Length}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/circle-perimeter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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