Circular Sector Area Calculator

The area equals one half times the radius squared times the central angle in radians, or 0.5 x r^2 x theta. Degrees are converted to radians first by multiplying by pi and dividing by 180.

The arc length equals the radius times the central angle in radians, r x theta. It measures the curved outer edge of the sector, not the straight chord across the ends.

The chord is the straight line joining the two end points of the arc. It equals 2 x r x sin(theta / 2), so at r = 10 and a 180 degree angle the chord is 20, the full diameter.

Both. Use the Degrees and Radians buttons to pick the unit that matches your angle, and the input label changes to confirm it. The tool also reports the angle in radians so you can check the conversion.

A sector is a slice of one circle, so its central angle cannot exceed 360 degrees or two pi radians. A value larger than a full turn is rejected with an error rather than wrapping around.

At exactly 360 degrees or two pi radians the sector becomes the whole disc, so the area equals pi r squared and the arc equals the full circumference. The chord collapses to zero because both ends meet at the same point.

The engine rounds each value to six decimal places, and the display trims trailing zeros. Whole results like a chord of 20 show without decimals, while irrational results such as an arc of 7.853982 keep six digits.

Yes. Both the radius and the angle must be greater than zero, or the tool shows an error. A zero or negative radius has no geometric sector, so those inputs are not accepted.

Yes. Everything runs in your browser with no data sent to a server, so your radius and angle values never leave your device.