Circle Segment Formulas

Posted In: Mathematics

In geometry, a circular segment (symbol: ⌓) is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord.

Segment of a Circle


Radius of circle: R
Arc length: s
Chord: a
Central angle (in radians): x
Central angle (in degrees): α
Height of the segment: h
Perimeter: L
Area: S

  1. $a=2√{2hR-h^2}$
  2. $h=R-1/2√{4R^2-a^2}, h < R$
  3. $L=s+a$
  4. $S=1/2(sR-a(R-h))=R^2/2({απ}/{180°}-sin\ α)=R^2/2(x-sin\ x),$
    S≈2/3ha

Post Tags: Geometry


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