Find the minor circular segment cut off by a chord and central angle. The result panel keeps segment area and its numerical trail together.
A minor segment equals sector area minus the isosceles triangle formed by the two radii and chord.
The roles assigned to radius and central angle in degrees explain the operation that produces segment area.
Convert θ to radians and use A=r²(θ−sinθ)/2. To continue from Circle Segment Area, try sector area.
This page uses angles from 0° through 180° for the minor segment. A major segment is the circle area minus the minor one.
For a Circle Segment Area audit, retain Radius and Central angle in degrees. Decide the likely direction of Segment area before rerunning Circle Segment Area. Change only Central angle in degrees; the response in Segment area can then be traced within the Circle Segment Area setup.
For r=10 and θ=90°, the sector area is 25π and the triangle area is 50, so the segment is about 28.54.
Increasing the angle enlarges the minor segment until it reaches a semicircle at 180°. That behavior gives the circle segment area output a built-in reasonableness test.
The Circle Segment Area meaning depends on Radius. The Circle Segment Area meaning also depends on Central angle in degrees. Carry those Circle Segment Area roles into any later Circle Segment Area work.
A sector includes the center; a segment is bounded by chord and arc. Writing “Segment area” beside the output prevents that mix-up.
Add the central triangle area back to the segment. The total must reproduce the corresponding sector area.
For Circle Segment Area, copying only the final number discards the assumptions that make it meaningful. Retain the inputs and one independent identity with the answer. This compact record is sufficient for a later review and prevents rounded output from becoming the source for an avoidable second-rounding error.
Segments describe circular caps in tanks, windows, machining, and geometric probability. A related application of Circle Segment Area is chord.
A chord and its arc.
The sector contains the central triangle in addition to the cap.
Subtract the minor segment from πr².