Home › Math & Conversions › Core Math & Algebra › Circular Segment Area Circular Segment Area Calculator Compute the area of a circular segment from radius and height, radius and central angle, or radius and chord length. The tool also reports chord length, arc length, sector area, and the segment’s share of the full circle. Input mode Radius and segment height (sagitta) Radius and central angle Radius and chord length Choose the quantities you know. All length inputs must use the same unit (e.g., meters, centimeters). Radius R Circle radius (R > 0). Segment height h Sagitta: distance from the chord up to the circle. Must satisfy 0 < h < 2R. Central angle θ Units: degrees radians Use 0 < θ < 360° (or 0 < θ < 2π radians) for a proper segment. Chord length c Straight-line distance between the chord endpoints. Must satisfy 0 < c < 2R. Calculate Clear Enter the known values and click Calculate to see segment area, chord and arc length, sector area, and more. What is a circular segment? A circular segment is the region of a circle cut off by a chord. It is bounded by: a straight line (the chord), and the corresponding arc of the circle. If you draw a chord across a circle and shade only the “cap” between the chord and the circle, you get a circular segment. In many applications (fluid levels in tanks, structural design, optics, surveying) we know the radius and one extra measure such as the segment height, chord length, or central angle and need the segment area. Key geometry and notation We will use the following notation: R – circle radius h – segment height (sagitta), measured from the chord to the circle along the symmetry axis c – chord length θ – central angle corresponding to the segment (in radians) A_seg – circular segment area A_sec – circular sector area Formulas for circular segment area The fundamental formula for the area of a circular segment in terms of radius and central angle (in radians) is: Segment area from radius and central angle Given a circle of radius R and central angle θ (radians), A_sec = (1/2) · R² · θ (sector area) A_tri = (1/2) · R² · sin θ (area of isosceles triangle formed by the two radii and the chord) A_seg = A_sec − A_tri = (R²

Subcategories in Home › Math & Conversions › Core Math & Algebra › Circular Segment Area Circular Segment Area Calculator Compute the area of a circular segment from radius and height, radius and central angle, or radius and chord length. The tool also reports chord length, arc length, sector area, and the segment’s share of the full circle. Input mode Radius and segment height (sagitta) Radius and central angle Radius and chord length Choose the quantities you know. All length inputs must use the same unit (e.g., meters, centimeters). Radius R Circle radius (R > 0). Segment height h Sagitta: distance from the chord up to the circle. Must satisfy 0 < h < 2R. Central angle θ Units: degrees radians Use 0 < θ < 360° (or 0 < θ < 2π radians) for a proper segment. Chord length c Straight-line distance between the chord endpoints. Must satisfy 0 < c < 2R. Calculate Clear Enter the known values and click Calculate to see segment area, chord and arc length, sector area, and more. What is a circular segment? A circular segment is the region of a circle cut off by a chord. It is bounded by: a straight line (the chord), and the corresponding arc of the circle. If you draw a chord across a circle and shade only the “cap” between the chord and the circle, you get a circular segment. In many applications (fluid levels in tanks, structural design, optics, surveying) we know the radius and one extra measure such as the segment height, chord length, or central angle and need the segment area. Key geometry and notation We will use the following notation: R – circle radius h – segment height (sagitta), measured from the chord to the circle along the symmetry axis c – chord length θ – central angle corresponding to the segment (in radians) A_seg – circular segment area A_sec – circular sector area Formulas for circular segment area The fundamental formula for the area of a circular segment in terms of radius and central angle (in radians) is: Segment area from radius and central angle Given a circle of radius R and central angle θ (radians), A_sec = (1/2) · R² · θ (sector area) A_tri = (1/2) · R² · sin θ (area of isosceles triangle formed by the two radii and the chord) A_seg = A_sec − A_tri = (R².