Circular segment area calculator
A circular segment is the part of a circle cut off by a straight line, like the water surface in a horizontal tank. Enter the radius and central angle.
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How to use it
- Enter radius, central angle and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Area = (r² ÷ 2) × (θ − sin θ) with θ in radians, chord = 2r × sin(θ ÷ 2), arc = r × θ and height = r × (1 − cos(θ ÷ 2)).
Example
Inputs: Radius = 10, Central angle = 90 °, Length unit = Centimeters (cm). Result: Segment area: 28.5398 cm²; Chord length: 14.1421 cm; Arc length: 15.708 cm.
Limits and caveats
- The angle is in degrees; angles above 180° give the major segment.
- The unit choice only labels the results.
Questions about this tool
What is the formula for the area of a circular segment?
The sector area minus the triangle formed by the two radii and the chord, which simplifies to (r² ÷ 2) × (θ − sin θ).
What are the minor and major segments?
A chord splits the circle in two. The minor segment has an angle under 180°; the major one is the rest, and together they make the full circle.
What is the segment height?
The greatest distance between the chord and the arc, also called the sagitta. It equals r × (1 − cos(θ ÷ 2)).