How to use the arc and sector calculator
- Enter the circle radius as a positive number.
- Enter the central angle in degrees from 0 through 360, including either endpoint.
- Calculate to see the length along the arc, the area swept by the two radii, and the straight chord between arc endpoints.
- Editing either input removes the confirmed answer and disables copying.
Arc, sector and chord formulas
The angle fraction is θ/360. Arc length is L=(θ/360)2πr, and sector area is A=(θ/360)πr².
The endpoint chord is c=2r sin(θ/2), with the degree angle converted to radians for the sine function.
At 0° the arc, area and chord are zero. At 360° the arc is the full circumference and area is the full circle, while both endpoints coincide so the chord is zero.
Worked examples
Radius 10, angle 90°
The quarter-circle arc is 5π≈15.71, the sector area is 25π≈78.54, and the chord is 10√2≈14.14.
Radius 6, angle 180°
The semicircular arc is 6π≈18.85, its sector area is 18π≈56.55, and the chord is the diameter, 12.
Limits and input rules
- Radius must be positive; the central angle may be zero but must not exceed 360°.
- This page calculates the selected directed fraction from 0° to 360°; it does not automatically replace a major arc with its minor arc.
- Chord is a straight endpoint distance, not the curved arc length, and sector area is not circular-segment area.
- All lengths share the radius unit. Display rounding does not add measurement accuracy.
Frequently asked questions
What is the difference between an arc and a chord?
An arc follows the circle; a chord is the straight line joining the same endpoints.
Can the central angle be 360°?
Yes. It gives a complete circle and a zero chord because the endpoints meet.
Is this circular-segment area?
No. A segment lies between a chord and arc; this tool returns the sector between two radii and the arc.