Calculators
Circular Sector Calculator
Calculate circular sector area, arc length, chord length, and perimeter from a radius and central angle in degrees.
Measure a sector of a circle.
A circular sector is the region between two radii and their circular arc. Enter radius r and central angle θ in degrees. Convert to radians with t = θπ/180. Sector area = r²t/2, arc length = rt, chord length = 2r sin(t/2), and sector perimeter = rt + 2r. For radius 5 and angle 90°, area is 6.25π ≈ 19.6349540849 square units, arc length is 2.5π ≈ 7.85398163397 units, and chord length is approximately 7.07106781187 units. Angles above 180° describe major sectors; the chord still joins the arc endpoints. At 360°, area and arc length describe a full circle and chord length is zero. The reported sector perimeter always includes two radii, including at 360°; use arc length alone for the circumference of a full disk. This is a sector calculator, not a circular segment calculator. Radius must be from 1e-50 to 1e50 and angle from 1e-10 to 360 degrees. Use consistent length units. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the sector area formula?
With the central angle in degrees, area = (θ/360)πr². With radians t, area = r²t/2.
How do arc length and chord length differ?
Arc length follows the circle boundary: rt. Chord length is the straight distance between the arc endpoints: 2r sin(t/2).
Can I calculate a major sector?
Yes. Enter an angle above 180° and up to 360°. The area and arc follow that larger angle; the chord connects its endpoints.
What happens at 360 degrees?
Area is the full circle area and arc length is its circumference. Chord length is zero. Sector perimeter here is defined as arc plus two radii even at 360°; for a disk boundary use arc length alone.
Which units and inputs should I use?
Enter a radius from 1e-50 to 1e50 and an angle from 1e-10 to 360 degrees. Lengths use your radius unit and area uses its square. Divide diameters by two before entering them. Calculations run locally in your browser.