What Is FREE TOOLS Segment Area Calculator?
A Segment Area Calculator is a free online tool used to calculate the area of a circular segment. A circular segment is the region of a circle enclosed by a chord and the corresponding arc.
Unlike a sector, which is bounded by two radii and an arc, a segment is bounded by one chord and one arc.
How Does a Segment Area Calculator Work?
When the radius and central angle are known, the area of a circular segment can be calculated using:
Segment Area = Sector Area − Triangle Area
For an angle in radians:
A = ½r²(θ − sin θ)
Where:
- A = segment area
- r = radius of the circle
- θ = central angle in radians
- sin θ = sine of the central angle
Example
Suppose a circle has:
- Radius = 10 cm
- Central angle = 90°
First convert 90° to radians:
90° = π/2 radians
Then:
A = ½(10²)(π/2 − sin(π/2))
A ≈ 28.54 cm²
Therefore, the circular segment has an area of approximately 28.54 square centimeters.
What Can a FREE Segment Area Calculator Calculate?
A Segment Area Calculator can help determine:
- Circular segment area
- Radius
- Central angle
- Chord-related measurements
- Segment height or sagitta
- Areas of minor circular segments
- Areas of major circular segments
- Measurements using degrees or radians
Why Use a Segment Area Calculator?
This free tool is useful for:
- Geometry homework
- Mathematics and science
- Engineering
- Architecture
- Construction
- Land surveying
- Mechanical design
- Circular structures and layouts
It can also reduce errors when calculating curved areas manually.
Segment vs. Sector
The two terms are easy to confuse:
- Sector: bounded by two radii and an arc.
- Segment: bounded by a chord and an arc.
For example, a pizza slice is typically a sector, while the curved portion cut off by a straight chord is a segment.
In simple terms:
A FREE Segment Area Calculator quickly finds the area of the portion of a circle between a chord and its curved arc, using measurements such as the radius, central angle, or segment height.
