What does this calculator measure?
A central angle selects part of a circle. Arc length measures its curved edge, while sector area measures the region between the radii and the arc. This tool uses radius and angle; it does not infer an angle from an arc or solve circular segments.
For related tasks, use the existing Circle Calculator or Polygon Area & Perimeter Calculator.
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Optional geometry sets (paid link) can help draw a manual dimension sketch. No purchase is required.
How to enter values and calculate
Choose one length unit, enter a positive radius, select degrees or radians, enter the central angle and Calculate. Radians accept ordinary numbers or forms such as pi/2, 3*pi/2 and 2*pi. Degree input is numeric. Unit changes convert the represented radius or valid angle.
The result and calculated drawing clear whenever an input changes. Reset returns the form to its initial state. Copy, Download and Print retain the result and calculation steps.
Optional graph paper notebooks (paid link) can help organize written working.
Formula and calculation method
θrad = θdeg × π/180; L = rθ; A = r²θ/2; chord = 2r sin(θ/2). For 0 < θ < 2π, sector boundary = L + 2r. At θ=0 the boundary is defined here as zero; at a full turn it is just 2πr.
Steps are generated from the actual inputs. Unsupported input receives an error instead of a guessed result.
Worked example and interpretation
For radius 6 cm and angle 60°, θ=π/3. Arc length is 2π ≈ 6.28318531 cm, sector area is 6π ≈ 18.8495559 cm², chord is 6 cm and boundary is 12 + 2π ≈ 18.2831853 cm. A 270° input highlights the larger, reflex sector; a 360° input highlights the full disk.
Use the same inputs on the calculator to reproduce these values and inspect the diagram.
Understand the result and diagram
The highlighted region follows the entered angle counterclockwise from the right-pointing radius. The whole reference circle remains faintly visible. Radius changes preserve the circle shape while its labels and numerical measurements change; the drawing is fitted to its box, not a physical-size image.
Optional protractors (paid link) can help with angle conventions and geometry practice. For two Cartesian points, the existing Distance & Midpoint Calculator provides a separate workflow.
Accuracy, input limits and assumptions
Radius must represent 10⁻⁹ to 10⁹ metres in the chosen unit. Angles must be within one nonnegative turn, including endpoints. Floating-point results use up to nine significant digits. No circular segment, inverse-angle solve, negative rotation or multi-turn winding is provided.
Optional geometry workbooks (paid link) can support additional practice. No measurement uncertainty, material allowance or construction design is inferred.
Circle Arc & Sector Calculator FAQs
Yes. Select degrees from 0 to 360 or radians from 0 to 2*pi. Radian input also accepts pi, pi/2 and 2*pi.
Yes. After Calculate it highlights the entered sector, including reflex angles and a complete circle.
No. An arc follows the circle; the chord is the straight line between its endpoints.
For an intermediate angle it is arc length plus two radii. This tool defines zero-angle boundary as zero and full-circle boundary as the circumference.
No. It calculates the sector, not the region bounded by a chord and an arc.
Yes. Length units convert the radius; angle-unit changes convert a valid current angle. Results and the calculated picture clear until Calculate is selected again.
Sources and methodology
Independently implemented standard geometry formulas, reviewed October 29, 2026. Sketches explain dimension conventions. Sources describe the mathematics; the linked organizations do not endorse this calculator.