What the formula is measuring
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.
Math calculator
Circle Segment Area Calculator
Find the minor circular segment cut off by a chord and central angle. The result panel keeps segment area and its numerical trail together.
Circle Segment Area inputs
Provide the numbers
Practical meaning
Segments describe circular caps in tanks, windows, machining, and geometric probability. A related application of Circle Segment Area is chord.
Mistakes worth catching
This page uses angles from 0° through 180° for the minor segment. A major segment is the circle area minus the minor one.
A rough estimate made before calculating gives the finished segment area a useful plausibility check.
A numerical walkthrough
For r=10 and θ=90°, the sector area is 25π and the triangle area is 50, so the segment is about 28.54.
Calculating it by hand
Convert θ to radians and use A=r²(θ−sinθ)/2. To continue from Circle Segment Area, try sector area.
What to record with the answer
Before entering radius and central angle in degrees, identify what each field represents. Its label determines how the circle segment area relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
How the output responds
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.
Precision and reporting
A final answer should carry enough context to be reusable: name it segment area, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied inputs in the fields and the displayed formula are more informative than the decimal alone.
A sector includes the center; a segment is bounded by chord and arc. Writing “Segment area” beside the output prevents that mix-up.
A useful note for this result contains the supplied inputs (radius and central angle in degrees), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
Preserving the setup for Circle Segment Area
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.
Questions about Circle Segment Area
What bounds a segment?
A chord and its arc.
Why subtract a triangle?
The sector contains the central triangle in addition to the cap.
How do I get the major segment?
Subtract the minor segment from πr².