Sector area
A = ½r²θ
With degrees: A = (θ/360)πr².
Circle Sector Calculator — Area, Arc Length, Radius and Angle
Enter Two Known Values
Sector Results
Radius—
Central angle—
Sector area—
Arc length—
Chord length—
Sector perimeter—
Enter two different positive measurements, then calculate to see the formula path.
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Circle Sector Formulas
A sector is the part of a circle bounded by two radii and their connecting arc. These formulas use the central angle θ in radians unless a degree formula is shown.
Arc length
s = rθ
With degrees: s = (θ/360)2πr.
Radius from area and arc
A = ½rs, so r = 2A/s.
Then find the angle with θ = s/r.
Chord and perimeter
Chord: c = 2r sin(θ/2).
Sector perimeter: P = 2r + s.
Assumption: This calculator models a Euclidean circle sector within one complete turn, so
0 < θ ≤ 360° (or 0 < θ ≤ 2π radians). It supports minor sectors, semicircles, major sectors, and a full circle.
How to Use the Sector Calculator
- Select two different known values: radius, central angle, sector area, or arc length.
- Enter positive numbers and choose the shared length unit. Area automatically uses the square of that unit.
- Choose degrees or radians for angle inputs and displayed angles.
- Select Calculate sector. Review the formula path, then copy or download the results if useful.
The calculator uses the selected length unit consistently. For example, a radius in centimetres produces arc, chord, and perimeter in centimetres and area in square centimetres.
Worked Circle Sector Examples
Radius 10 cm and angle 90°
Convert 90° to π/2 radians.
A = ½(10²)(π/2) = 25π ≈ 78.540 cm².
s = 10(π/2) = 5π ≈ 15.708 cm.
Area 50 m² and arc 10 m
r = 2A/s = 2(50)/10 = 10 m.
θ = s/r = 10/10 = 1 rad ≈ 57.296°.
Angle 120° and arc 8 ft
120° = 2π/3 rad.
r = s/θ = 8/(2π/3) ≈ 3.820 ft.
A = ½rs ≈ 15.279 ft².
Common Sector Calculation Mistakes
Using degrees in a radian formula
The compact formulas A = ½r²θ and s = rθ require radians. Convert degrees with θrad = θdeg × π/180.
Confusing arc and chord
Arc length follows the curved edge. Chord length is the straight line between the arc endpoints, so it is shorter except in the limiting tiny-angle case.
Forgetting square units
Radius, arc, chord, and perimeter use length units. Sector area uses square units such as cm² or ft².
Circle Sector Calculator FAQs
What two values can I use to solve a circle sector?
You can use any two different values from radius, central angle, sector area, and arc length. The calculator derives the other values from that pair.
How do you find sector area from radius and angle?
In radians, use A = ½r²θ. In degrees, use A = (θ/360)πr².
How do you find arc length from radius and angle?
In radians, use s = rθ. In degrees, use s = (θ/360)2πr.
Can I find radius from sector area and arc length?
Yes. Because A = ½rs, rearrange the formula to r = 2A/s. The angle is then θ = s/r in radians.
What is the perimeter of a sector?
The sector perimeter is the arc length plus two radii: P = s + 2r. It is not the same as the chord length.
Does this calculator support major sectors and full circles?
Yes. It supports one-turn sectors with a central angle greater than 0 and up to 360 degrees, including minor sectors, semicircles, major sectors, and a full circle.
Are my measurements uploaded?
No. The calculation runs locally in your browser and the page does not send your sector measurements to a server.
Calculation Notes
Last reviewed: July 30, 2026 by the Starlight Tools editorial team.
The formulas are standard Euclidean sector relationships. Calculations use JavaScript's full floating-point value of π and retain unrounded values until display. Decimal places affect on-page formatting; the CSV keeps unrounded numeric values for reuse.