Sector Area Calculator

A circle sector is the region bounded by two radii and the arc connecting their endpoints. It resembles a slice of pie, and its size depends on both the radius of the circle and the central angle between the two radii. This sector area calculator combines those measurements to determine how much two-dimensional space the slice covers. The answer is expressed in square units because area is a two-dimensional measurement. When the angle is supplied in degrees, sector area equals the central angle divided by 360, multiplied by pi and the square of the radius. This works because the angle divided by 360 is the fraction of the full circle included in the sector. A 90-degree sector occupies one quarter of a circle, a 180-degree sector occupies one half, and a 360-degree sector is the complete circle. Multiplying that fraction by the full circle area gives the sector area. Radians provide a more direct formula. If the central angle is theta radians, the sector area equals one half times the radius squared times theta. A full circle measures 2 pi radians, so substituting 2 pi into this formula produces pi times radius squared, exactly the standard circle area. The calculator supports either convention and applies the matching formula automatically after you select the angle unit. Use consistent length units for the radius. A radius entered in centimeters produces an area in square centimeters, while meters produce square meters. The numeric answer does not attach a particular unit because the same geometry works for millimeters, feet, miles, or any other length scale. If you convert the radius before calculating, remember that area conversion factors are squared; doubling a radius makes the sector area four times as large. Sector calculations appear in geometry exercises, circular gardens, mechanical parts, architectural curves, pizza portions, fan-shaped graphics, and material estimates. The calculator accepts angles larger than a full turn as well, which can be useful in cumulative rotation problems, although ordinary geometric sectors usually use angles from zero through one full revolution. Results are rounded for readability while calculations retain double-precision accuracy. Check that the radius is positive and that the selected angle unit matches your source measurement before using the result in further work.