Sector and Segment Area Calculator

Radius (r) Central angle or chord length Angle unit

Notes: Provide radius and either a central angle or a chord length. If both are given, central angle takes precedence. Angle may be in degrees or radians (select above).

Circle geometry may appear intricate, particularly for students, engineers, architects, and math lovers. Concepts such as sector, segment, chord, and arc can seem daunting until you simplify them with clear definitions and formulas.

What Is a Sector?

A sector of a circle is a portion formed by two radii and the arc between them. It is defined by the central angle (θ), which means the larger the angle, the larger the sector area.

What Is a Segment?

A segment of a circle is the region enclosed by a chord and its corresponding arc.

Types of segments:

Minor segment (smaller area)
Major segment (larger area)

What Is an Arc?

An arc is a curved portion of the circumference of a circle. The arc’s length depends on the radius and the central angle.

What Is a Chord?

A chord is a straight line joining two points on the circle. Every chord creates a segment in the circle.

Formulae You Need to Know

Arc Length

If θ is in degrees:

Arc Length = \frac{θ}{360} \times 2 π r

If θ is in radians:

Arc Length = r θ

Chord Length

Chord Length = 2 r \cdot \sin (\frac{θ}{2})

Where:

$r$ = radius
$θ$ = central angle in radians (use θ° × π/180)

Sector Area

If θ is in degrees:

Sector Area = \frac{θ}{360} \times π r^{2}

If θ is in radians:

Sector Area = \frac{1}{2} r^{2} θ

Segment Area

Segment area = Sector area − Triangle area formed by the radii and chord.

Segment Area = \frac{1}{2} r^{2} (θ - \sin θ)

(θ in radians)

How to find the Sector and Segment Area using our Calculator?

Enter the “Radius”, “Central Angle”, and select the “Angle Unit”.
Click “Calculate,” and the calculator computes the Arc Length, Chord Length, Sector Area, and Segment Area.