Finds the area of a circular segment — the region between a chord and the arc it cuts off — distinct from a sector, which includes the triangle formed by the two radii.
How it works
The sector’s area (found from the radius and central angle) has the triangular portion (formed by the chord and the two radii) subtracted from it.
What this does not include
This does not include a sector’s full area — for that pizza-slice shape (which includes the triangular portion), use this site’s sector area calculator instead.
How to use this calculator
- Enter the circle’s radius and the central angle of the segment.
A worked example
A circular segment with radius 5 and a 90° central angle: area = 7.135 — the sector area minus the triangular portion.
Radius 10, 180° angle: area = 157.0796 — at exactly 180°, the segment becomes a full semicircle.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Circle’s radius |
| Angle | Central angle spanning the segment, in degrees |
Edge cases worth knowing
A segment is the sector minus its triangular piece — the curved sliver between a chord and the arc, distinct from a sector, which includes the full pie-slice triangle.
At 180°, the segment area equals a plain semicircle — the second example above confirms this, since the “triangle” being subtracted degenerates to a straight line with zero area at that angle.
Frequently asked questions
What’s the difference between a sector and a segment?
A sector is the full pizza-slice shape bounded by two radii and an arc; a segment is only the region between a chord and the arc, without the triangular wedge back to the center.
What happens at a 180° angle?
The segment becomes exactly half the circle, since the chord is the diameter and there’s no triangle left to subtract.
What’s a real-world example of a segment?
The cross-section of liquid in a partially filled cylindrical tank lying on its side is a classic segment-area problem.
