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Circular Segment Area

Also known as area of a segment · chord segment area · partially filled pipe area

A=r22(θ−sin⁡θ)A = \frac{r^2}{2}(\theta - \sin\theta)

Worked example: half disc, r = 1 m, theta = 180 deg → pi/2 m^2 — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
π=3.141592653589793\pi = 3.141592653589793Pi · exact
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Circular Segment Area explained

θrA

A segment is what a straight chord cuts off a circle — the shape above the waterline in a partly filled pipe, or the sliver of a porthole below a fluid level. It is the sector minus the triangle formed by the two radii, which after simplification gives A=12r2(θ−sin⁡θ)A = \tfrac{1}{2}r^2(\theta - \sin\theta) with θ\theta in radians. Degrees entered here are converted automatically, but the formula itself is a radians-only expression.

Two checks: at θ=π\theta = \pi (180°) the segment is exactly half the disc, and the formula returns πr2/2\pi r^2/2. At θ=2π\theta = 2\pi it returns the whole circle. Tank gaugers use this constantly — the volume of liquid in a horizontal cylindrical tank is this segment area times the tank length.

Circular Segment Area formula

A=r22(θ−sin⁡θ)A = \frac{r^2}{2}(\theta - \sin\theta)
Where
  • AA= Segment area (m²)
  • rr= Radius (m)
  • θ\theta= Central angle (°)

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