Segment Area Calculator
Calculate the area of a circular segment - the region between a chord and the arc. Formula: Segment = Sector - Triangle.
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Frequently Asked Questions
What is a circular segment?
A circular segment is the region between a chord and the arc it cuts off. It's the area you get when you cut a circle with a straight line that doesn't go through the center.
What is the formula for segment area?
A = ½r²(θ - sin θ) where θ is in radians. This equals the sector area minus the triangle area formed by the two radii and the chord.
How is a segment different from a sector?
A sector includes the two radii from the center (like a pizza slice), while a segment is only the area between the chord and the arc (without the triangular part near the center).
Why do we subtract the triangle area?
The sector includes both the segment and the triangle formed by the two radii and chord. To get just the segment, we calculate the sector area and subtract the triangle area.
What is a major vs minor segment?
A minor segment has a central angle less than 180° (smaller piece), while a major segment has a central angle greater than 180° (larger piece).
Can segment area be negative?
No, segment area is always positive. For very small angles, the segment area approaches zero, and for 180°, it equals half the circle.
What is the segment area for a semicircle?
For a 180° angle, the segment is exactly half the circle with area πr²/2, because the triangle area becomes zero (the chord is the diameter).
Where are segment calculations used?
Segment calculations are used in architecture (arched windows, bridges), engineering (tank volume calculations), astronomy (eclipse coverage), and many geometric problems.