Arc Length and Sector Area Calculator

This calculator finds the arc length, sector area and chord length of a circular sector when you enter the radius and the central angle. A sector is the pie-slice-shaped region bounded by two straight radii and the curved arc between them. The three measurements this calculator returns capture its full geometry: the arc length (the curved boundary), the sector area (the enclosed space) and the chord length (the straight line connecting the two arc endpoints). Arc length equals radius times central angle in radians, and since radians equal degrees times pi divided by 180, you can enter the angle in either unit and the calculator handles the conversion. Sector area equals one half times radius squared times the central angle in radians, which is the same as the fraction of the full circle area determined by the angle. Chord length equals two times the radius times the sine of half the central angle in radians. The calculator also shows the angle in both degrees and radians so you always have the radian measure to hand for further calculations. You enter the radius and the central angle, select degrees or radians, and all three results appear immediately. The tool is useful for students solving circle geometry problems at NCEA Level 2 or above, engineers calculating bend allowances and cutting lengths for curved parts, architects laying out circular floor plans, and anyone working with sectors in practical geometry. All inputs must be positive; the central angle must be between 0 and 360 degrees (or 0 and 2pi radians). Results are rounded to two decimal places and are suitable for planning and checking purposes.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.