Math
Circle Segment Area Calculator
Use this circle segment area calculator for the region cut off by a chord when you know the radius and central angle.
Segment area
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- Segment area
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- Sector area
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- Center triangle term
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- Arc length
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Study path
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What the circle segment area calculator solves
Use this circle segment area calculator for the region cut off by a chord when you know the radius and central angle.
Formula
How to use it
- Enter the circle radius.
- Enter the central angle in degrees.
- Compare the segment area with the sector and center-triangle areas.
How to read the answer
For angles below 180 degrees, the segment is the small cap between chord and arc. Angles above 180 degrees describe the larger segment.
Common mistakes and edge cases
- Convert degrees to radians before checking the formula by hand.
- Use radius, not diameter.
- Do not confuse segment area with sector area.
Worked examples
Quarter-circle segment
Segment area
Segment area = 18.2655 square units
Large segment
Segment area
Segment area = 63.1852 square units
Invalid angle
Segment area
Error
Frequently asked questions
What is a circle segment?+
It is the region between a chord and the matching arc of the circle.
How is segment area different from sector area?+
A sector includes the triangle from the center to the chord. A segment subtracts the signed triangle term, which adds area for angles over 180 degrees.
Can I use degrees?+
Yes. Enter degrees here; the calculator converts the angle to radians for the formula.
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Last updated: May 15, 2026