The Segment Area Calculator is an online tool that helps you calculate the area of a circular segment quickly and accurately. A circular segment is the region of a circle bounded by a chord and the corresponding arc. By entering values such as radius and angle (or chord length), this calculator provides instant results without manual calculations.
It is ideal for geometry problems, engineering designs, and real-world applications where only a portion of a circle is involved.
A circular segment is the area between a chord (a straight line cutting across a circle) and the arc it subtends. Unlike a sector, a segment does not include the triangle formed by two radii.
In simple terms:
A sector uses two radii
A segment uses one chord and one arc
Segment area is smaller than sector area for the same angle
The Segment Area Calculator uses the standard formula based on the central angle (in radians).
Segment Area Formula
Segment Area = (1/2) × r² × (θ − sin θ)
Where:
r = radius of the circle
θ = central angle in radians
sin θ = sine of the angle
This formula is widely used in mathematics, physics, and engineering.Example:
Find the segment area of a circle with a radius of 6 cm and a central angle of 60°.
Solution:
Convert angle to radians
θ = 60° × (π ÷ 180) = π/3
Apply the formula
Segment Area = (1/2) × 6² × (π/3 − sin(π/3))
Calculate
Segment Area ≈ 4.07 cm²
Final Answer: The segment area is 4.07 cm².