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Circle Segment Area Calculator

Find the area between a chord and an arc

Circle Segment Area Formula

A = r²(θ - sin θ) / 2

A circular segment is the area cut off by a chord. The formula subtracts the isosceles triangle area from the sector area, using θ in radians.

⚠Enter angle in degrees. This calculator uses the minor segment formula for central angles in standard position.

How Circle Segment Area Works

A segment is part of a sector. Removing the triangle formed by two radii and the chord leaves the curved segment area.

Sector

The larger slice bounded by two radii.

Triangle

The straight-sided part under the chord.

Segment

Sector minus triangle.

Radians

The formula uses angle in radians.

💡 Example: For r=10 and θ=60°, A≈9.058.

Applications of Circle Segment Area

Tank LevelsArchesLensesCircular Design

Frequently Asked Questions

What is a circle segment area calculator?▼

It calculates the area between a chord and an arc of a circle.

What is the circular segment area formula?▼

For angle θ in radians, A=r²(θ-sinθ)/2.

How do I use this calculator?▼

Enter radius and central angle in degrees, then click Calculate.

Is segment area the same as sector area?▼

No. Segment area equals sector area minus the triangle area.

Where is circular segment area used?▼

It is used in tanks, lenses, arches, fluid levels, and circular design.

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