What Is a FREE Segment Area Calculator?
A FREE Segment Area Calculator is an online tool that calculates the area of a circular segment—the region of a circle enclosed by a chord and the arc above or below that chord.
It is useful for geometry, construction, engineering, architecture, landscaping, surveying, and design when you need to calculate a portion of a circle that is not a complete sector.
What Is a Circular Segment?
A circular segment is the area between a straight chord and the corresponding circular arc.
It is different from a sector:
- Sector: bounded by two radii and an arc
- Segment: bounded by one chord and an arc
Circular Segment Area Formula
When the central angle θ is measured in radians, the minor segment area is:
A = ½r²(θ − sin θ)
Where:
- A = segment area
- r = radius
- θ = central angle in radians
If the angle is provided in degrees, it must first be converted to radians:
θ (radians) = θ (degrees) × π ÷ 180
Example
Suppose a circle has:
- Radius = 10 inches
- Central angle = 90°
Convert 90° to radians:
90° = π/2 radians
Then:
A = ½ × 10² × (π/2 − sin(π/2))
A ≈ 28.54 square inches
Therefore, the circular segment area is approximately 28.54 square inches.
What Can a FREE Segment Area Calculator Calculate?
Depending on the calculator, you may be able to enter:
- Circle radius
- Diameter
- Central angle
- Segment height (sagitta)
- Chord length
The calculator can then determine:
- Segment area
- Chord length
- Arc length
- Segment height
- Central angle
- Other related circular measurements
Segment Area Using Segment Height
Some calculators allow you to calculate the segment area using the radius and segment height (also called the sagitta).
The segment height is the perpendicular distance from the midpoint of the chord to the arc.
This is particularly useful when the central angle is not directly known.
Segment vs. Sector
| Feature | Circular Segment | Circular Sector |
|---|---|---|
| Straight boundary | Chord | Two radii |
| Curved boundary | Arc | Arc |
| Main inputs | Radius, angle, chord, or height | Radius and central angle |
| Shape | Arc cut off by a chord | Pie-slice shape |
Common Uses of a FREE Segment Area Calculator
A Segment Area Calculator can be useful for:
Construction
Calculate curved sections of walls, arches, windows, roofs, and structural components.
Engineering
Determine the area of circular sections used in mechanical and structural designs.
Architecture
Calculate curved architectural elements and circular design features.
Landscaping
Estimate the area of curved garden beds, pathways, or other circular layouts.
Mathematics
Help students understand circle geometry, chords, arcs, sectors, and segments.
Manufacturing
Calculate material requirements for components containing curved sections.
Why Use a FREE Segment Area Calculator?
Calculating a circular segment manually can involve trigonometric functions and several steps. A free calculator performs the calculation automatically, helping users save time and reduce errors.
Key Benefit
A FREE Segment Area Calculator provides a fast and convenient way to determine the area of a circular segment using measurements such as radius, central angle, chord length, or segment height.
It is especially useful for geometry, construction, engineering, architecture, manufacturing, landscaping, and technical design projects.
Explore circular segment calculations
