Sector Area Calculator

Calculate the area of a sector using the central angle and radius below and learn the formula and steps to solve it below.

Results:

Sector Area

 

Arc Length (s)

 

Chord Length (a)

 


How to Calculate Sector Area

A sector is a pie-slice shaped portion of a circle surrounded by two radii edges and bounded by the circle’s outer arc.

diagram of a sector showing the radius, central angle, chord length, and arc length

To calculate the area of a sector, a simple formula can be used.

Sector Area Formula

The area of a sector can be found using the formula:

sector area = r² × θ2

Thus, a sector’s area is equal to the radius r squared times the central angle θ in radians, divided by 2.

Trying to solve the area of a segment? Try our segment area calculator.

For example, find the area of a sector with a radius of 12 and a central angle of 1.5 radians.

sector area = 12² × 1.52
sector area = 144 × 1.52
sector area = 2162
sector area = 108

Thus, the area of the sector is 108.

You might also find our arc length calculator useful for solving the arc length of a sector.