Sector Area

\[A=\frac{1}{2}r^2\theta\]

Variables

Asector area (m²)

rcircle radius (m)

thetacentral angle in radians (rad)

The sector area formula calculates the area of a portion of a circle defined by a central angle.

A sector is the region enclosed by two radii and the corresponding arc of the circle.

This formula uses the radius and the central angle measured in radians.

Use this formula when:

- Calculating partial areas of circles

- Working with circular geometry

- Designing mechanical or rotating components

- Analyzing pie-shaped regions

- Solving engineering and physics problems involving rotation

The angle must be expressed in radians for direct application of the formula.

If:

r = 4 m

theta = 1.5 rad

Then:

A = (4²*1.5)/2

A = (16*1.5)/2

A = 12 m²

- Geometry and trigonometry

- Mechanical engineering

- Architecture and design

- Rotational systems

- Physics calculations

- Computer graphics and modeling