Use this geometry calculation when the shape, dimensions, coordinate system, and units match the stated ideal Euclidean model.

Radius

Circle radius.

Central angle (rad)

Central angle in radians between zero and 2π.

Calculate the area of a circular segment as (r²/2)·(θ−sin θ) for a central angle in radians. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Segment area

The resulting segment area returned as a number.

• The result assumes exact idealized geometry. Measurement uncertainty, rounded inputs, nonplanarity, self-intersection, thickness, curved coordinate systems, and ambiguous dimension definitions are not automatically represented.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Sketch and label the dimensions, verify unit consistency, and use coordinate or CAD methods for irregular measured shapes.

• Circle Arc Length Calculator

  Compute the arc length of a circular segment from its central angle and radius.

• Circle Sector Area Calculator

  Compute the area of a circular sector from its central angle and radius.

• Annulus Area Calculator

  Calculate the area of an annulus from its outer and inner radii as π(R²−r²).